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StirlingCycB.tbl.md

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StirlingCycB

['A028338', 'A039757', 'A039758', 'A109692']

StirlingCycB Triangle view

Row Seq
Row0 [1]
Row1 [1, 1]
Row2 [3, 4, 1]
Row3 [15, 23, 9, 1]
Row4 [105, 176, 86, 16, 1]
Row5 [945, 1689, 950, 230, 25, 1]
Row6 [10395, 19524, 12139, 3480, 505, 36, 1]
Row7 [135135, 264207, 177331, 57379, 10045, 973, 49, 1]
Row8 [2027025, 4098240, 2924172, 1038016, 208054, 24640, 1708, 64, 1]
Row9 [34459425, 71697105, 53809164, 20570444, 4574934, 626934, 53676, 2796, 81, 1]

StirlingCycB Triangles

Flat Seq
Triangle [[1], [1, 1], [3, 4, 1], [15, 23, 9, 1], [105, 176, 86, 16, 1], [945, 1689, 950, 230, 25, 1], [10395, 19524, 12139, 3480, 505, 36, 1], [135135, 264207, 177331, 57379, 10045, 973, 49, 1], [2027025, 4098240, 2924172, 1038016, 208054, 24640, 1708, 64, 1], [34459425, 71697105, 53809164, 20570444, 4574934, 626934, 53676, 2796, 81, 1]]
RevTabl [[1], [1, 1], [1, 4, 3], [1, 9, 23, 15], [1, 16, 86, 176, 105], [1, 25, 230, 950, 1689, 945], [1, 36, 505, 3480, 12139, 19524, 10395], [1, 49, 973, 10045, 57379, 177331, 264207, 135135], [1, 64, 1708, 24640, 208054, 1038016, 2924172, 4098240, 2027025], [1, 81, 2796, 53676, 626934, 4574934, 20570444, 53809164, 71697105, 34459425]]
AntiDiag [[1], [1], [3, 1], [15, 4], [105, 23, 1], [945, 176, 9], [10395, 1689, 86, 1], [135135, 19524, 950, 16], [2027025, 264207, 12139, 230, 1], [34459425, 4098240, 177331, 3480, 25]]
AccTabl [[1], [1, 2], [3, 7, 8], [15, 38, 47, 48], [105, 281, 367, 383, 384], [945, 2634, 3584, 3814, 3839, 3840], [10395, 29919, 42058, 45538, 46043, 46079, 46080], [135135, 399342, 576673, 634052, 644097, 645070, 645119, 645120], [2027025, 6125265, 9049437, 10087453, 10295507, 10320147, 10321855, 10321919, 10321920], [34459425, 106156530, 159965694, 180536138, 185111072, 185738006, 185791682, 185794478, 185794559, 185794560]]
RevAccTabl [[1], [2, 1], [8, 7, 3], [48, 47, 38, 15], [384, 383, 367, 281, 105], [3840, 3839, 3814, 3584, 2634, 945], [46080, 46079, 46043, 45538, 42058, 29919, 10395], [645120, 645119, 645070, 644097, 634052, 576673, 399342, 135135], [10321920, 10321919, 10321855, 10320147, 10295507, 10087453, 9049437, 6125265, 2027025], [185794560, 185794559, 185794478, 185791682, 185738006, 185111072, 180536138, 159965694, 106156530, 34459425]]
AccRevTabl [[1], [1, 2], [1, 5, 8], [1, 10, 33, 48], [1, 17, 103, 279, 384], [1, 26, 256, 1206, 2895, 3840], [1, 37, 542, 4022, 16161, 35685, 46080], [1, 50, 1023, 11068, 68447, 245778, 509985, 645120], [1, 65, 1773, 26413, 234467, 1272483, 4196655, 8294895, 10321920], [1, 82, 2878, 56554, 683488, 5258422, 25828866, 79638030, 151335135, 185794560]]
DiffxTabl [[1], [1, 2], [3, 8, 3], [15, 46, 27, 4], [105, 352, 258, 64, 5], [945, 3378, 2850, 920, 125, 6], [10395, 39048, 36417, 13920, 2525, 216, 7], [135135, 528414, 531993, 229516, 50225, 5838, 343, 8], [2027025, 8196480, 8772516, 4152064, 1040270, 147840, 11956, 512, 9], [34459425, 143394210, 161427492, 82281776, 22874670, 3761604, 375732, 22368, 729, 10]]

StirlingCycB Row sums

Trait Seq
RowSum [1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560]
EvenSum [1, 1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280]
OddSum [0, 1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280]
AltSum [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
AbsSum [1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560]
AccSum [1, 3, 18, 148, 1520, 18656, 266112, 4324608, 78870528, 1595142144]
AccRevSum [1, 3, 14, 92, 784, 8224, 102528, 1481472, 24348672, 448598016]
DiagSum [1, 1, 4, 19, 129, 1130, 12171, 155625, 2303602, 38738501]

StirlingCycB Transforms

Trans Seq
RowLcm [1, 1, 12, 1035, 794640, 2324992950, 4810656157072920, 182911242997871793405, 409032268138980471585600, 11760264404154296455873489887669723900]
RowGcd [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 4, 23, 176, 1689, 19524, 264207, 4098240, 71697105]
CentralE [1, 4, 86, 3480, 208054]
CentralO [1, 23, 950, 57379, 4574934]
ColMiddle [1, 1, 4, 23, 86, 950, 3480, 57379, 208054, 4574934]
ColLeft [1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 2, 12, 112, 1390, 21316, 387016, 8089152, 190810614, 5004826108]
InvBinConv [1, 0, -4, 28, -146, 176, 13096, -332856, 6220278, -100254944]
TransSqrs [0, 1, 8, 68, 680, 7984, 108416, 1676800, 29146624, 563014656]
TransNat0 [0, 1, 6, 44, 400, 4384, 56448, 836352, 14026752, 262803456]
TransNat1 [1, 3, 14, 92, 784, 8224, 102528, 1481472, 24348672, 448598016]
PosHalf [1, 3, 21, 231, 3465, 65835, 1514205, 40883535, 1267389585, 44358635475]
NegHalf [1, -1, 5, -45, 585, -9945, 208845, -5221125, 151412625, -4996616625]

StirlingCycB Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
DiagRow2 [3, 23, 86, 230, 505, 973, 1708, 2796, 4335, 6435]
DiagRow3 [15, 176, 950, 3480, 10045, 24640, 53676, 106800, 197835, 345840]
DiagRow4 [105, 1689, 12139, 57379, 208054, 626934, 1646778, 3889578, 8439783, 17085783]
DiagRow5 [945, 19524, 177331, 1038016, 4574934, 16486680, 51069018, 140529312, 351523887, 812840028]
DiagRow6 [10395, 264207, 2924172, 20570444, 107494190, 453714470, 1628301884, 5141534684, 14632679633, 38205040445]
DiagRow7 [135135, 4098240, 53809164, 444647600, 2702025590, 13137458400, 53845005500, 192666441968, 617014151325, 1801370405120]
DiagRow8 [2027025, 71697105, 1094071221, 10431670821, 72578259391, 401014719391, 1854829867891, 7442156684963, 26569595376038, 86014818744998]
DiagRow9 [34459425, 1396704420, 24372200061, 264300628944, 2078757113719, 12906154537276, 66696220706115, 297403077939968, 1174199725349222, 4184718381424152]

StirlingCycB Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425]
DiagCol1 [1, 4, 23, 176, 1689, 19524, 264207, 4098240, 71697105, 1396704420]
DiagCol2 [1, 9, 86, 950, 12139, 177331, 2924172, 53809164, 1094071221, 24372200061]
DiagCol3 [1, 16, 230, 3480, 57379, 1038016, 20570444, 444647600, 10431670821, 264300628944]
DiagCol4 [1, 25, 505, 10045, 208054, 4574934, 107494190, 2702025590, 72578259391, 2078757113719]
DiagCol5 [1, 36, 973, 24640, 626934, 16486680, 453714470, 13137458400, 401014719391, 12906154537276]
DiagCol6 [1, 49, 1708, 53676, 1646778, 51069018, 1628301884, 53845005500, 1854829867891, 66696220706115]
DiagCol7 [1, 64, 2796, 106800, 3889578, 140529312, 5141534684, 192666441968, 7442156684963, 297403077939968]
DiagCol8 [1, 81, 4335, 197835, 8439783, 351523887, 14632679633, 617014151325, 26569595376038, 1174199725349222]
DiagCol9 [1, 100, 6435, 345840, 17085783, 812840028, 38205040445, 1801370405120, 86014818744998, 4184718381424152]

StirlingCycB Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
PolyRow2 [3, 8, 15, 24, 35, 48, 63, 80, 99, 120]
PolyRow3 [15, 48, 105, 192, 315, 480, 693, 960, 1287, 1680]
PolyRow4 [105, 384, 945, 1920, 3465, 5760, 9009, 13440, 19305, 26880]
PolyRow5 [945, 3840, 10395, 23040, 45045, 80640, 135135, 215040, 328185, 483840]
PolyRow6 [10395, 46080, 135135, 322560, 675675, 1290240, 2297295, 3870720, 6235515, 9676800]
PolyRow7 [135135, 645120, 2027025, 5160960, 11486475, 23224320, 43648605, 77414400, 130945815, 212889600]
PolyRow8 [2027025, 10321920, 34459425, 92897280, 218243025, 464486400, 916620705, 1703116800, 3011753745, 5109350400]
PolyRow9 [34459425, 185794560, 654729075, 1857945600, 4583103525, 10218700800, 21082276215, 40874803200, 75293843625, 132843110400]

StirlingCycB Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425]
PolyCol1 [1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560]
PolyCol2 [1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, 654729075]
PolyCol3 [1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280, 1857945600]
PolyCol4 [1, 5, 35, 315, 3465, 45045, 675675, 11486475, 218243025, 4583103525]
PolyCol5 [1, 6, 48, 480, 5760, 80640, 1290240, 23224320, 464486400, 10218700800]
PolyCol6 [1, 7, 63, 693, 9009, 135135, 2297295, 43648605, 916620705, 21082276215]
PolyCol7 [1, 8, 80, 960, 13440, 215040, 3870720, 77414400, 1703116800, 40874803200]
PolyCol8 [1, 9, 99, 1287, 19305, 328185, 6235515, 130945815, 3011753745, 75293843625]
PolyCol9 [1, 10, 120, 1680, 26880, 483840, 9676800, 212889600, 5109350400, 132843110400]

StirlingCycB:Inv

[]

StirlingCycB:Inv Triangle view

Row Seq
Row0 [1]
Row1 [-1, 1]
Row2 [1, -4, 1]
Row3 [-1, 13, -9, 1]
Row4 [1, -40, 58, -16, 1]
Row5 [-1, 121, -330, 170, -25, 1]
Row6 [1, -364, 1771, -1520, 395, -36, 1]
Row7 [-1, 1093, -9219, 12411, -5075, 791, -49, 1]
Row8 [1, -3280, 47188, -96096, 58086, -13776, 1428, -64, 1]
Row9 [-1, 9841, -239220, 719860, -618870, 209622, -32340, 2388, -81, 1]

StirlingCycB:Inv Triangles

Flat Seq
Triangle [[1], [-1, 1], [1, -4, 1], [-1, 13, -9, 1], [1, -40, 58, -16, 1], [-1, 121, -330, 170, -25, 1], [1, -364, 1771, -1520, 395, -36, 1], [-1, 1093, -9219, 12411, -5075, 791, -49, 1], [1, -3280, 47188, -96096, 58086, -13776, 1428, -64, 1], [-1, 9841, -239220, 719860, -618870, 209622, -32340, 2388, -81, 1]]
RevTabl [[1], [1, -1], [1, -4, 1], [1, -9, 13, -1], [1, -16, 58, -40, 1], [1, -25, 170, -330, 121, -1], [1, -36, 395, -1520, 1771, -364, 1], [1, -49, 791, -5075, 12411, -9219, 1093, -1], [1, -64, 1428, -13776, 58086, -96096, 47188, -3280, 1], [1, -81, 2388, -32340, 209622, -618870, 719860, -239220, 9841, -1]]
AntiDiag [[1], [-1], [1, 1], [-1, -4], [1, 13, 1], [-1, -40, -9], [1, 121, 58, 1], [-1, -364, -330, -16], [1, 1093, 1771, 170, 1], [-1, -3280, -9219, -1520, -25]]
AccTabl [[1], [-1, 0], [1, -3, -2], [-1, 12, 3, 4], [1, -39, 19, 3, 4], [-1, 120, -210, -40, -65, -64], [1, -363, 1408, -112, 283, 247, 248], [-1, 1092, -8127, 4284, -791, 0, -49, -48], [1, -3279, 43909, -52187, 5899, -7877, -6449, -6513, -6512], [-1, 9840, -229380, 490480, -128390, 81232, 48892, 51280, 51199, 51200]]
RevAccTabl [[1], [0, -1], [-2, -3, 1], [4, 3, 12, -1], [4, 3, 19, -39, 1], [-64, -65, -40, -210, 120, -1], [248, 247, 283, -112, 1408, -363, 1], [-48, -49, 0, -791, 4284, -8127, 1092, -1], [-6512, -6513, -6449, -7877, 5899, -52187, 43909, -3279, 1], [51200, 51199, 51280, 48892, 81232, -128390, 490480, -229380, 9840, -1]]
AccRevTabl [[1], [1, 0], [1, -3, -2], [1, -8, 5, 4], [1, -15, 43, 3, 4], [1, -24, 146, -184, -63, -64], [1, -35, 360, -1160, 611, 247, 248], [1, -48, 743, -4332, 8079, -1140, -47, -48], [1, -63, 1365, -12411, 45675, -50421, -3233, -6513, -6512], [1, -80, 2308, -30032, 179590, -439280, 280580, 41360, 51201, 51200]]
DiffxTabl [[1], [-1, 2], [1, -8, 3], [-1, 26, -27, 4], [1, -80, 174, -64, 5], [-1, 242, -990, 680, -125, 6], [1, -728, 5313, -6080, 1975, -216, 7], [-1, 2186, -27657, 49644, -25375, 4746, -343, 8], [1, -6560, 141564, -384384, 290430, -82656, 9996, -512, 9], [-1, 19682, -717660, 2879440, -3094350, 1257732, -226380, 19104, -729, 10]]

StirlingCycB:Inv Row sums

Trait Seq
RowSum [1, 0, -2, 4, 4, -64, 248, -48, -6512, 51200]
EvenSum [1, -1, 2, -10, 60, -356, 2168, -14344, 106704, -890512]
OddSum [0, 1, -4, 14, -56, 292, -1920, 14296, -113216, 941712]
AltSum [1, -2, 6, -24, 116, -648, 4088, -28640, 219920, -1832224]
AbsSum [1, 2, 6, 24, 116, 648, 4088, 28640, 219920, 1832224]
AccSum [1, -1, -4, 18, -12, -260, 1712, -3640, -33008, 426352]
AccRevSum [1, 1, -4, 2, 36, -188, 272, 3208, -32112, 136848]
DiagSum [1, -1, 2, -5, 15, -50, 181, -711, 3036, -14045]

StirlingCycB:Inv Transforms

Trans Seq
RowLcm [1, 1, 4, 117, 2320, 308550, 24881416560, 3415119838107075, 10927777609869120, 8184449743464324553963740]
RowGcd [1, 1, 4, 1, 2, 1, 1, 1, 2, 1]
RowMax [1, 1, 4, 13, 58, 330, 1771, 12411, 96096, 719860]
CentralE [1, -4, 58, -1520, 58086]
CentralO [-1, 13, -330, 12411, -618870]
ColMiddle [1, -1, -4, 13, 58, -330, -1520, 12411, 58086, -618870]
ColLeft [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 0, -6, 12, 126, -1120, -308, 87080, -752314, -2251680]
InvBinConv [1, 2, 10, 68, 574, 5732, 65292, 830216, 11606854, 176361980]
TransSqrs [0, 1, 0, -14, 64, -44, -1504, 12776, -46080, -182000]
TransNat0 [0, 1, -2, -2, 32, -124, 24, 3256, -25600, 85648]
TransNat1 [1, 1, -4, 2, 36, -188, 272, 3208, -32112, 136848]
PosHalf [1, -1, -3, 27, -103, -105, 6101, -64141, 350129, 1270447]
NegHalf [1, 3, 13, 79, 601, 5339, 53861, 607527, 7560625, 102637235]

StirlingCycB:Inv Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [-1, -4, -9, -16, -25, -36, -49, -64, -81, -100]
DiagRow2 [1, 13, 58, 170, 395, 791, 1428, 2388, 3765, 5665]
DiagRow3 [-1, -40, -330, -1520, -5075, -13776, -32340, -68160, -132165, -239800]
DiagRow4 [1, 121, 1771, 12411, 58086, 209622, 630042, 1652442, 3899247, 8455447]
DiagRow5 [-1, -364, -9219, -96096, -618870, -2924712, -11115258, -35901888, -102189087, -262842580]
DiagRow6 [1, 1093, 47188, 719860, 6289690, 38461522, 182959876, 721488196, 2458702675, 7452711695]
DiagRow7 [-1, -3280, -239220, -5278240, -61885450, -484962192, -2863440580, -13685763520, -55483708995, -197085231200]
DiagRow8 [1, 9841, 1205941, 38153621, 595122671, 5929706783, 43154434323, 248440887123, 1191663940038, 4936283332838]
DiagRow9 [-1, -29524, -6059229, -273134576, -5629238615, -70856013228, -631863659427, -4358476966272, -24616763946918, -118406147270840]

StirlingCycB:Inv Diagonals as columns

DiagCol Seq
DiagCol0 [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]
DiagCol1 [1, -4, 13, -40, 121, -364, 1093, -3280, 9841, -29524]
DiagCol2 [1, -9, 58, -330, 1771, -9219, 47188, -239220, 1205941, -6059229]
DiagCol3 [1, -16, 170, -1520, 12411, -96096, 719860, -5278240, 38153621, -273134576]
DiagCol4 [1, -25, 395, -5075, 58086, -618870, 6289690, -61885450, 595122671, -5629238615]
DiagCol5 [1, -36, 791, -13776, 209622, -2924712, 38461522, -484962192, 5929706783, -70856013228]
DiagCol6 [1, -49, 1428, -32340, 630042, -11115258, 182959876, -2863440580, 43154434323, -631863659427]
DiagCol7 [1, -64, 2388, -68160, 1652442, -35901888, 721488196, -13685763520, 248440887123, -4358476966272]
DiagCol8 [1, -81, 3765, -132165, 3899247, -102189087, 2458702675, -55483708995, 1191663940038, -24616763946918]
DiagCol9 [1, -100, 5665, -239800, 8455447, -262842580, 7452711695, -197085231200, 4936283332838, -118406147270840]

StirlingCycB:Inv Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]
PolyRow2 [1, -2, -3, -2, 1, 6, 13, 22, 33, 46]
PolyRow3 [-1, 4, -3, -16, -29, -36, -31, -8, 39, 116]
PolyRow4 [1, 4, 41, 52, 1, -124, -311, -524, -703, -764]
PolyRow5 [-1, -64, -87, 200, 707, 1104, 941, -232, -2745, -6688]
PolyRow6 [1, 248, -571, -2216, -2047, 2456, 11893, 23864, 32609, 29368]
PolyRow7 [-1, -48, 5701, 3008, -22365, -61136, -77143, -19104, 157543, 463760]
PolyRow8 [1, -6512, -14575, 85264, 221185, 108176, -531887, -1679600, -2797951, -2783600]
PolyRow9 [-1, 51200, -156655, -742624, 119171, 3888704, 8562965, 7725920, -7135609, -41382784]

StirlingCycB:Inv Polynomial values as columns

PolyCol Seq
PolyCol0 [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]
PolyCol1 [1, 0, -2, 4, 4, -64, 248, -48, -6512, 51200]
PolyCol2 [1, 1, -3, -3, 41, -87, -571, 5701, -14575, -156655]
PolyCol3 [1, 2, -2, -16, 52, 200, -2216, 3008, 85264, -742624]
PolyCol4 [1, 3, 1, -29, 1, 707, -2047, -22365, 221185, 119171]
PolyCol5 [1, 4, 6, -36, -124, 1104, 2456, -61136, 108176, 3888704]
PolyCol6 [1, 5, 13, -31, -311, 941, 11893, -77143, -531887, 8562965]
PolyCol7 [1, 6, 22, -8, -524, -232, 23864, -19104, -1679600, 7725920]
PolyCol8 [1, 7, 33, 39, -703, -2745, 32609, 157543, -2797951, -7135609]
PolyCol9 [1, 8, 46, 116, -764, -6688, 29368, 463760, -2783600, -41382784]

StirlingCycB:Rev

[]

StirlingCycB:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 1]
Row2 [1, 4, 3]
Row3 [1, 9, 23, 15]
Row4 [1, 16, 86, 176, 105]
Row5 [1, 25, 230, 950, 1689, 945]
Row6 [1, 36, 505, 3480, 12139, 19524, 10395]
Row7 [1, 49, 973, 10045, 57379, 177331, 264207, 135135]
Row8 [1, 64, 1708, 24640, 208054, 1038016, 2924172, 4098240, 2027025]
Row9 [1, 81, 2796, 53676, 626934, 4574934, 20570444, 53809164, 71697105, 34459425]

StirlingCycB:Rev Triangles

Flat Seq
Triangle [[1], [1, 1], [1, 4, 3], [1, 9, 23, 15], [1, 16, 86, 176, 105], [1, 25, 230, 950, 1689, 945], [1, 36, 505, 3480, 12139, 19524, 10395], [1, 49, 973, 10045, 57379, 177331, 264207, 135135], [1, 64, 1708, 24640, 208054, 1038016, 2924172, 4098240, 2027025], [1, 81, 2796, 53676, 626934, 4574934, 20570444, 53809164, 71697105, 34459425]]
RevTabl [[1], [1, 1], [3, 4, 1], [15, 23, 9, 1], [105, 176, 86, 16, 1], [945, 1689, 950, 230, 25, 1], [10395, 19524, 12139, 3480, 505, 36, 1], [135135, 264207, 177331, 57379, 10045, 973, 49, 1], [2027025, 4098240, 2924172, 1038016, 208054, 24640, 1708, 64, 1], [34459425, 71697105, 53809164, 20570444, 4574934, 626934, 53676, 2796, 81, 1]]
AntiDiag [[1], [1], [1, 1], [1, 4], [1, 9, 3], [1, 16, 23], [1, 25, 86, 15], [1, 36, 230, 176], [1, 49, 505, 950, 105], [1, 64, 973, 3480, 1689]]
AccTabl [[1], [1, 2], [1, 5, 8], [1, 10, 33, 48], [1, 17, 103, 279, 384], [1, 26, 256, 1206, 2895, 3840], [1, 37, 542, 4022, 16161, 35685, 46080], [1, 50, 1023, 11068, 68447, 245778, 509985, 645120], [1, 65, 1773, 26413, 234467, 1272483, 4196655, 8294895, 10321920], [1, 82, 2878, 56554, 683488, 5258422, 25828866, 79638030, 151335135, 185794560]]
RevAccTabl [[1], [2, 1], [8, 5, 1], [48, 33, 10, 1], [384, 279, 103, 17, 1], [3840, 2895, 1206, 256, 26, 1], [46080, 35685, 16161, 4022, 542, 37, 1], [645120, 509985, 245778, 68447, 11068, 1023, 50, 1], [10321920, 8294895, 4196655, 1272483, 234467, 26413, 1773, 65, 1], [185794560, 151335135, 79638030, 25828866, 5258422, 683488, 56554, 2878, 82, 1]]
AccRevTabl [[1], [1, 2], [3, 7, 8], [15, 38, 47, 48], [105, 281, 367, 383, 384], [945, 2634, 3584, 3814, 3839, 3840], [10395, 29919, 42058, 45538, 46043, 46079, 46080], [135135, 399342, 576673, 634052, 644097, 645070, 645119, 645120], [2027025, 6125265, 9049437, 10087453, 10295507, 10320147, 10321855, 10321919, 10321920], [34459425, 106156530, 159965694, 180536138, 185111072, 185738006, 185791682, 185794478, 185794559, 185794560]]
DiffxTabl [[1], [1, 2], [1, 8, 9], [1, 18, 69, 60], [1, 32, 258, 704, 525], [1, 50, 690, 3800, 8445, 5670], [1, 72, 1515, 13920, 60695, 117144, 72765], [1, 98, 2919, 40180, 286895, 1063986, 1849449, 1081080], [1, 128, 5124, 98560, 1040270, 6228096, 20469204, 32785920, 18243225], [1, 162, 8388, 214704, 3134670, 27449604, 143993108, 430473312, 645273945, 344594250]]

StirlingCycB:Rev Row sums

Trait Seq
RowSum [1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560]
EvenSum [1, 1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280]
OddSum [0, 1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280]
AltSum [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
AbsSum [1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560]
AccSum [1, 3, 14, 92, 784, 8224, 102528, 1481472, 24348672, 448598016]
AccRevSum [1, 3, 18, 148, 1520, 18656, 266112, 4324608, 78870528, 1595142144]
DiagSum [1, 1, 2, 5, 13, 40, 127, 443, 1610, 6207]

StirlingCycB:Rev Transforms

Trans Seq
RowLcm [1, 1, 12, 1035, 794640, 2324992950, 4810656157072920, 182911242997871793405, 409032268138980471585600, 11760264404154296455873489887669723900]
RowGcd [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 4, 23, 176, 1689, 19524, 264207, 4098240, 71697105]
CentralE [1, 4, 86, 3480, 208054]
CentralO [1, 9, 230, 10045, 626934]
ColMiddle [1, 1, 4, 9, 86, 230, 3480, 10045, 208054, 626934]
ColLeft [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight [1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425]
BinConv [1, 2, 12, 112, 1390, 21316, 387016, 8089152, 190810614, 5004826108]
InvBinConv [1, 0, -4, -28, -146, -176, 13096, 332856, 6220278, 100254944]
TransSqrs [0, 1, 16, 236, 3624, 60144, 1089920, 21578752, 465321472, 10881911808]
TransNat0 [0, 1, 10, 100, 1136, 14816, 220032, 3679488, 68548608, 1409347584]
TransNat1 [1, 3, 18, 148, 1520, 18656, 266112, 4324608, 78870528, 1595142144]
PosHalf [1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, 654729075]
NegHalf [1, -1, -1, -3, -15, -105, -945, -10395, -135135, -2027025]

StirlingCycB:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425]
DiagRow1 [1, 4, 23, 176, 1689, 19524, 264207, 4098240, 71697105, 1396704420]
DiagRow2 [1, 9, 86, 950, 12139, 177331, 2924172, 53809164, 1094071221, 24372200061]
DiagRow3 [1, 16, 230, 3480, 57379, 1038016, 20570444, 444647600, 10431670821, 264300628944]
DiagRow4 [1, 25, 505, 10045, 208054, 4574934, 107494190, 2702025590, 72578259391, 2078757113719]
DiagRow5 [1, 36, 973, 24640, 626934, 16486680, 453714470, 13137458400, 401014719391, 12906154537276]
DiagRow6 [1, 49, 1708, 53676, 1646778, 51069018, 1628301884, 53845005500, 1854829867891, 66696220706115]
DiagRow7 [1, 64, 2796, 106800, 3889578, 140529312, 5141534684, 192666441968, 7442156684963, 297403077939968]
DiagRow8 [1, 81, 4335, 197835, 8439783, 351523887, 14632679633, 617014151325, 26569595376038, 1174199725349222]
DiagRow9 [1, 100, 6435, 345840, 17085783, 812840028, 38205040445, 1801370405120, 86014818744998, 4184718381424152]

StirlingCycB:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
DiagCol2 [3, 23, 86, 230, 505, 973, 1708, 2796, 4335, 6435]
DiagCol3 [15, 176, 950, 3480, 10045, 24640, 53676, 106800, 197835, 345840]
DiagCol4 [105, 1689, 12139, 57379, 208054, 626934, 1646778, 3889578, 8439783, 17085783]
DiagCol5 [945, 19524, 177331, 1038016, 4574934, 16486680, 51069018, 140529312, 351523887, 812840028]
DiagCol6 [10395, 264207, 2924172, 20570444, 107494190, 453714470, 1628301884, 5141534684, 14632679633, 38205040445]
DiagCol7 [135135, 4098240, 53809164, 444647600, 2702025590, 13137458400, 53845005500, 192666441968, 617014151325, 1801370405120]
DiagCol8 [2027025, 71697105, 1094071221, 10431670821, 72578259391, 401014719391, 1854829867891, 7442156684963, 26569595376038, 86014818744998]
DiagCol9 [34459425, 1396704420, 24372200061, 264300628944, 2078757113719, 12906154537276, 66696220706115, 297403077939968, 1174199725349222, 4184718381424152]

StirlingCycB:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
PolyRow2 [1, 8, 21, 40, 65, 96, 133, 176, 225, 280]
PolyRow3 [1, 48, 231, 640, 1365, 2496, 4123, 6336, 9225, 12880]
PolyRow4 [1, 384, 3465, 14080, 39585, 89856, 177289, 316800, 525825, 824320]
PolyRow5 [1, 3840, 65835, 394240, 1464645, 4133376, 9750895, 20275200, 38385225, 67594240]
PolyRow6 [1, 46080, 1514205, 13404160, 65909025, 231469056, 653309965, 1581465600, 3416285025, 6759424000]
PolyRow7 [1, 645120, 40883535, 536166400, 3493178325, 15276957696, 51611487235, 145494835200, 358709927625, 797612032000]
PolyRow8 [1, 10321920, 1267389585, 24663654400, 213083877825, 1161048784896, 4696645338385, 15422452531200, 43403901242625, 108475236352000]
PolyRow9 [1, 185794560, 44358635475, 1282510028800, 14702787569925, 99850195501056, 483754469853655, 1850694303744000, 5946334470239625, 16705186398208000]

StirlingCycB:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560]
PolyCol2 [1, 3, 21, 231, 3465, 65835, 1514205, 40883535, 1267389585, 44358635475]
PolyCol3 [1, 4, 40, 640, 14080, 394240, 13404160, 536166400, 24663654400, 1282510028800]
PolyCol4 [1, 5, 65, 1365, 39585, 1464645, 65909025, 3493178325, 213083877825, 14702787569925]
PolyCol5 [1, 6, 96, 2496, 89856, 4133376, 231469056, 15276957696, 1161048784896, 99850195501056]
PolyCol6 [1, 7, 133, 4123, 177289, 9750895, 653309965, 51611487235, 4696645338385, 483754469853655]
PolyCol7 [1, 8, 176, 6336, 316800, 20275200, 1581465600, 145494835200, 15422452531200, 1850694303744000]
PolyCol8 [1, 9, 225, 9225, 525825, 38385225, 3416285025, 358709927625, 43403901242625, 5946334470239625]
PolyCol9 [1, 10, 280, 12880, 824320, 67594240, 6759424000, 797612032000, 108475236352000, 16705186398208000]

StirlingCycB:Inv:Rev

[]

StirlingCycB:Inv:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, -1]
Row2 [1, -4, 1]
Row3 [1, -9, 13, -1]
Row4 [1, -16, 58, -40, 1]
Row5 [1, -25, 170, -330, 121, -1]
Row6 [1, -36, 395, -1520, 1771, -364, 1]
Row7 [1, -49, 791, -5075, 12411, -9219, 1093, -1]
Row8 [1, -64, 1428, -13776, 58086, -96096, 47188, -3280, 1]
Row9 [1, -81, 2388, -32340, 209622, -618870, 719860, -239220, 9841, -1]

StirlingCycB:Inv:Rev Triangles

Flat Seq
Triangle [[1], [1, -1], [1, -4, 1], [1, -9, 13, -1], [1, -16, 58, -40, 1], [1, -25, 170, -330, 121, -1], [1, -36, 395, -1520, 1771, -364, 1], [1, -49, 791, -5075, 12411, -9219, 1093, -1], [1, -64, 1428, -13776, 58086, -96096, 47188, -3280, 1], [1, -81, 2388, -32340, 209622, -618870, 719860, -239220, 9841, -1]]
RevTabl [[1], [-1, 1], [1, -4, 1], [-1, 13, -9, 1], [1, -40, 58, -16, 1], [-1, 121, -330, 170, -25, 1], [1, -364, 1771, -1520, 395, -36, 1], [-1, 1093, -9219, 12411, -5075, 791, -49, 1], [1, -3280, 47188, -96096, 58086, -13776, 1428, -64, 1], [-1, 9841, -239220, 719860, -618870, 209622, -32340, 2388, -81, 1]]
AntiDiag [[1], [1], [1, -1], [1, -4], [1, -9, 1], [1, -16, 13], [1, -25, 58, -1], [1, -36, 170, -40], [1, -49, 395, -330, 1], [1, -64, 791, -1520, 121]]
AccTabl [[1], [1, 0], [1, -3, -2], [1, -8, 5, 4], [1, -15, 43, 3, 4], [1, -24, 146, -184, -63, -64], [1, -35, 360, -1160, 611, 247, 248], [1, -48, 743, -4332, 8079, -1140, -47, -48], [1, -63, 1365, -12411, 45675, -50421, -3233, -6513, -6512], [1, -80, 2308, -30032, 179590, -439280, 280580, 41360, 51201, 51200]]
RevAccTabl [[1], [0, 1], [-2, -3, 1], [4, 5, -8, 1], [4, 3, 43, -15, 1], [-64, -63, -184, 146, -24, 1], [248, 247, 611, -1160, 360, -35, 1], [-48, -47, -1140, 8079, -4332, 743, -48, 1], [-6512, -6513, -3233, -50421, 45675, -12411, 1365, -63, 1], [51200, 51201, 41360, 280580, -439280, 179590, -30032, 2308, -80, 1]]
AccRevTabl [[1], [-1, 0], [1, -3, -2], [-1, 12, 3, 4], [1, -39, 19, 3, 4], [-1, 120, -210, -40, -65, -64], [1, -363, 1408, -112, 283, 247, 248], [-1, 1092, -8127, 4284, -791, 0, -49, -48], [1, -3279, 43909, -52187, 5899, -7877, -6449, -6513, -6512], [-1, 9840, -229380, 490480, -128390, 81232, 48892, 51280, 51199, 51200]]
DiffxTabl [[1], [1, -2], [1, -8, 3], [1, -18, 39, -4], [1, -32, 174, -160, 5], [1, -50, 510, -1320, 605, -6], [1, -72, 1185, -6080, 8855, -2184, 7], [1, -98, 2373, -20300, 62055, -55314, 7651, -8], [1, -128, 4284, -55104, 290430, -576576, 330316, -26240, 9], [1, -162, 7164, -129360, 1048110, -3713220, 5039020, -1913760, 88569, -10]]

StirlingCycB:Inv:Rev Row sums

Trait Seq
RowSum [1, 0, -2, 4, 4, -64, 248, -48, -6512, 51200]
EvenSum [1, 1, 2, 14, 60, 292, 2168, 14296, 106704, 941712]
OddSum [0, -1, -4, -10, -56, -356, -1920, -14344, -113216, -890512]
AltSum [1, 2, 6, 24, 116, 648, 4088, 28640, 219920, 1832224]
AbsSum [1, 2, 6, 24, 116, 648, 4088, 28640, 219920, 1832224]
AccSum [1, 1, -4, 2, 36, -188, 272, 3208, -32112, 136848]
AccRevSum [1, -1, -4, 18, -12, -260, 1712, -3640, -33008, 426352]
DiagSum [1, 1, 0, -3, -7, -2, 33, 95, 18, -671]

StirlingCycB:Inv:Rev Transforms

Trans Seq
RowLcm [1, 1, 4, 117, 2320, 308550, 24881416560, 3415119838107075, 10927777609869120, 8184449743464324553963740]
RowGcd [1, 1, 4, 1, 2, 1, 1, 1, 2, 1]
RowMax [1, 1, 4, 13, 58, 330, 1771, 12411, 96096, 719860]
CentralE [1, -4, 58, -1520, 58086]
CentralO [1, -9, 170, -5075, 209622]
ColMiddle [1, 1, -4, -9, 58, 170, -1520, -5075, 58086, 209622]
ColLeft [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]
BinConv [1, 0, -6, 12, 126, -1120, -308, 87080, -752314, -2251680]
InvBinConv [1, -2, 10, -68, 574, -5732, 65292, -830216, 11606854, -176361980]
TransSqrs [0, -1, 0, 34, -128, -404, 7136, -35160, -53248, 2423536]
TransNat0 [0, -1, -2, 14, -16, -196, 1464, -3592, -26496, 375152]
TransNat1 [1, -1, -4, 18, -12, -260, 1712, -3640, -33008, 426352]
PosHalf [1, 1, -3, -3, 41, -87, -571, 5701, -14575, -156655]
NegHalf [1, -3, 13, -71, 457, -3355, 27509, -248127, 2434129, -25741939]

StirlingCycB:Inv:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]
DiagRow1 [1, -4, 13, -40, 121, -364, 1093, -3280, 9841, -29524]
DiagRow2 [1, -9, 58, -330, 1771, -9219, 47188, -239220, 1205941, -6059229]
DiagRow3 [1, -16, 170, -1520, 12411, -96096, 719860, -5278240, 38153621, -273134576]
DiagRow4 [1, -25, 395, -5075, 58086, -618870, 6289690, -61885450, 595122671, -5629238615]
DiagRow5 [1, -36, 791, -13776, 209622, -2924712, 38461522, -484962192, 5929706783, -70856013228]
DiagRow6 [1, -49, 1428, -32340, 630042, -11115258, 182959876, -2863440580, 43154434323, -631863659427]
DiagRow7 [1, -64, 2388, -68160, 1652442, -35901888, 721488196, -13685763520, 248440887123, -4358476966272]
DiagRow8 [1, -81, 3765, -132165, 3899247, -102189087, 2458702675, -55483708995, 1191663940038, -24616763946918]
DiagRow9 [1, -100, 5665, -239800, 8455447, -262842580, 7452711695, -197085231200, 4936283332838, -118406147270840]

StirlingCycB:Inv:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [-1, -4, -9, -16, -25, -36, -49, -64, -81, -100]
DiagCol2 [1, 13, 58, 170, 395, 791, 1428, 2388, 3765, 5665]
DiagCol3 [-1, -40, -330, -1520, -5075, -13776, -32340, -68160, -132165, -239800]
DiagCol4 [1, 121, 1771, 12411, 58086, 209622, 630042, 1652442, 3899247, 8455447]
DiagCol5 [-1, -364, -9219, -96096, -618870, -2924712, -11115258, -35901888, -102189087, -262842580]
DiagCol6 [1, 1093, 47188, 719860, 6289690, 38461522, 182959876, 721488196, 2458702675, 7452711695]
DiagCol7 [-1, -3280, -239220, -5278240, -61885450, -484962192, -2863440580, -13685763520, -55483708995, -197085231200]
DiagCol8 [1, 9841, 1205941, 38153621, 595122671, 5929706783, 43154434323, 248440887123, 1191663940038, 4936283332838]
DiagCol9 [-1, -29524, -6059229, -273134576, -5629238615, -70856013228, -631863659427, -4358476966272, -24616763946918, -118406147270840]

StirlingCycB:Inv:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 0, -1, -2, -3, -4, -5, -6, -7, -8]
PolyRow2 [1, -2, -3, -2, 1, 6, 13, 22, 33, 46]
PolyRow3 [1, 4, 27, 64, 109, 156, 199, 232, 249, 244]
PolyRow4 [1, 4, -103, -524, -1439, -3004, -5351, -8588, -12799, -18044]
PolyRow5 [1, -64, -105, 2104, 11453, 35376, 83731, 168680, 304569, 507808]
PolyRow6 [1, 248, 6101, 18136, -6367, -195304, -802907, -2250184, -5164639, -10419272]
PolyRow7 [1, -48, -64141, -570368, -2114835, -4667344, -5955233, 919584, 30625337, 109501840]
PolyRow8 [1, -6512, 350129, 8227600, 55216705, 215770256, 610205233, 1375888144, 2590253825, 4129348240]
PolyRow9 [1, 51200, 1270447, -68107040, -908247811, -5406000704, -21409041365, -65535116128, -167440283015, -373575072896]

StirlingCycB:Inv:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 0, -2, 4, 4, -64, 248, -48, -6512, 51200]
PolyCol2 [1, -1, -3, 27, -103, -105, 6101, -64141, 350129, 1270447]
PolyCol3 [1, -2, -2, 64, -524, 2104, 18136, -570368, 8227600, -68107040]
PolyCol4 [1, -3, 1, 109, -1439, 11453, -6367, -2114835, 55216705, -908247811]
PolyCol5 [1, -4, 6, 156, -3004, 35376, -195304, -4667344, 215770256, -5406000704]
PolyCol6 [1, -5, 13, 199, -5351, 83731, -802907, -5955233, 610205233, -21409041365]
PolyCol7 [1, -6, 22, 232, -8588, 168680, -2250184, 919584, 1375888144, -65535116128]
PolyCol8 [1, -7, 33, 249, -12799, 304569, -5164639, 30625337, 2590253825, -167440283015]
PolyCol9 [1, -8, 46, 244, -18044, 507808, -10419272, 109501840, 4129348240, -373575072896]