Skip to content

Latest commit

 

History

History
369 lines (318 loc) · 21.4 KB

BinomialCatalan.tbl.md

File metadata and controls

369 lines (318 loc) · 21.4 KB
Raw

BinomialCatalan

['A124644', 'A098474']

BinomialCatalan Triangle view

Row Seq
Row0 [1]
Row1 [1, 1]
Row2 [1, 2, 2]
Row3 [1, 3, 6, 5]
Row4 [1, 4, 12, 20, 14]
Row5 [1, 5, 20, 50, 70, 42]
Row6 [1, 6, 30, 100, 210, 252, 132]
Row7 [1, 7, 42, 175, 490, 882, 924, 429]
Row8 [1, 8, 56, 280, 980, 2352, 3696, 3432, 1430]
Row9 [1, 9, 72, 420, 1764, 5292, 11088, 15444, 12870, 4862]

BinomialCatalan Triangles

Flat Seq
Triangle [[1], [1, 1], [1, 2, 2], [1, 3, 6, 5], [1, 4, 12, 20, 14], [1, 5, 20, 50, 70, 42], [1, 6, 30, 100, 210, 252, 132], [1, 7, 42, 175, 490, 882, 924, 429], [1, 8, 56, 280, 980, 2352, 3696, 3432, 1430], [1, 9, 72, 420, 1764, 5292, 11088, 15444, 12870, 4862]]
RevTabl [[1], [1, 1], [2, 2, 1], [5, 6, 3, 1], [14, 20, 12, 4, 1], [42, 70, 50, 20, 5, 1], [132, 252, 210, 100, 30, 6, 1], [429, 924, 882, 490, 175, 42, 7, 1], [1430, 3432, 3696, 2352, 980, 280, 56, 8, 1], [4862, 12870, 15444, 11088, 5292, 1764, 420, 72, 9, 1]]
AntiDiag [[1], [1], [1, 1], [1, 2], [1, 3, 2], [1, 4, 6], [1, 5, 12, 5], [1, 6, 20, 20], [1, 7, 30, 50, 14], [1, 8, 42, 100, 70]]
AccTabl [[1], [1, 2], [1, 3, 5], [1, 4, 10, 15], [1, 5, 17, 37, 51], [1, 6, 26, 76, 146, 188], [1, 7, 37, 137, 347, 599, 731], [1, 8, 50, 225, 715, 1597, 2521, 2950], [1, 9, 65, 345, 1325, 3677, 7373, 10805, 12235], [1, 10, 82, 502, 2266, 7558, 18646, 34090, 46960, 51822]]
RevAccTabl [[1], [2, 1], [5, 3, 1], [15, 10, 4, 1], [51, 37, 17, 5, 1], [188, 146, 76, 26, 6, 1], [731, 599, 347, 137, 37, 7, 1], [2950, 2521, 1597, 715, 225, 50, 8, 1], [12235, 10805, 7373, 3677, 1325, 345, 65, 9, 1], [51822, 46960, 34090, 18646, 7558, 2266, 502, 82, 10, 1]]
AccRevTabl [[1], [1, 2], [2, 4, 5], [5, 11, 14, 15], [14, 34, 46, 50, 51], [42, 112, 162, 182, 187, 188], [132, 384, 594, 694, 724, 730, 731], [429, 1353, 2235, 2725, 2900, 2942, 2949, 2950], [1430, 4862, 8558, 10910, 11890, 12170, 12226, 12234, 12235], [4862, 17732, 33176, 44264, 49556, 51320, 51740, 51812, 51821, 51822]]
DiffxTabl [[1], [1, 2], [1, 4, 6], [1, 6, 18, 20], [1, 8, 36, 80, 70], [1, 10, 60, 200, 350, 252], [1, 12, 90, 400, 1050, 1512, 924], [1, 14, 126, 700, 2450, 5292, 6468, 3432], [1, 16, 168, 1120, 4900, 14112, 25872, 27456, 12870], [1, 18, 216, 1680, 8820, 31752, 77616, 123552, 115830, 48620]]

BinomialCatalan Row sums

Trait Seq
RowSum [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822]
EvenSum [1, 1, 3, 7, 27, 91, 373, 1457, 6163, 25795]
OddSum [0, 1, 2, 8, 24, 97, 358, 1493, 6072, 26027]
AltSum [1, 0, 1, -1, 3, -6, 15, -36, 91, -232]
AbsSum [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822]
AccSum [1, 3, 9, 30, 111, 443, 1859, 8067, 35835, 161937]
AccRevSum [1, 3, 11, 45, 195, 873, 3989, 18483, 86515, 408105]
DiagSum [1, 1, 2, 3, 6, 11, 23, 47, 102, 221]

BinomialCatalan Transforms

Trans Seq
RowLcm [1, 1, 2, 30, 420, 2100, 69300, 6306300, 1681680, 257297040]
RowGcd [1, 1, 2, 1, 2, 1, 2, 1, 2, 1]
RowMax [1, 1, 2, 6, 20, 70, 252, 924, 3696, 15444]
CentralE [1, 2, 12, 100, 980]
CentralO [1, 3, 20, 175, 1764]
ColMiddle [1, 1, 2, 3, 12, 20, 100, 175, 980, 1764]
ColLeft [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]
BinConv [1, 2, 7, 33, 183, 1118, 7281, 49626, 349999, 2535078]
InvBinConv [1, 0, -1, -5, -9, 16, 185, 624, 175, -9080]
TransSqrs [0, 1, 10, 72, 456, 2705, 15438, 85925, 469976, 2538027]
TransNat0 [0, 1, 6, 30, 144, 685, 3258, 15533, 74280, 356283]
TransNat1 [1, 3, 11, 45, 195, 873, 3989, 18483, 86515, 408105]
PosHalf [1, 3, 10, 37, 150, 654, 3012, 14445, 71398, 361114]
NegHalf [1, -1, 2, -3, 6, -10, 20, -35, 70, -126]

BinomialCatalan Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]
DiagRow1 [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
DiagRow2 [1, 3, 12, 50, 210, 882, 3696, 15444, 64350, 267410]
DiagRow3 [1, 4, 20, 100, 490, 2352, 11088, 51480, 235950, 1069640]
DiagRow4 [1, 5, 30, 175, 980, 5292, 27720, 141570, 707850, 3476330]
DiagRow5 [1, 6, 42, 280, 1764, 10584, 60984, 339768, 1840410, 9733724]
DiagRow6 [1, 7, 56, 420, 2940, 19404, 121968, 736164, 4294290, 24334310]
DiagRow7 [1, 8, 72, 600, 4620, 33264, 226512, 1472328, 9202050, 55621280]
DiagRow8 [1, 9, 90, 825, 6930, 54054, 396396, 2760615, 18404100, 118195220]
DiagRow9 [1, 10, 110, 1100, 10010, 84084, 660660, 4907760, 34763300, 236390440]

BinomialCatalan Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
DiagCol2 [2, 6, 12, 20, 30, 42, 56, 72, 90, 110]
DiagCol3 [5, 20, 50, 100, 175, 280, 420, 600, 825, 1100]
DiagCol4 [14, 70, 210, 490, 980, 1764, 2940, 4620, 6930, 10010]
DiagCol5 [42, 252, 882, 2352, 5292, 10584, 19404, 33264, 54054, 84084]
DiagCol6 [132, 924, 3696, 11088, 27720, 60984, 121968, 226512, 396396, 660660]
DiagCol7 [429, 3432, 15444, 51480, 141570, 339768, 736164, 1472328, 2760615, 4907760]
DiagCol8 [1430, 12870, 64350, 235950, 707850, 1840410, 4294290, 9202050, 18404100, 34763300]
DiagCol9 [4862, 48620, 267410, 1069640, 3476330, 9733724, 24334310, 55621280, 118195220, 236390440]

BinomialCatalan 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, 5, 13, 25, 41, 61, 85, 113, 145, 181]
PolyRow3 [1, 15, 71, 199, 429, 791, 1315, 2031, 2969, 4159]
PolyRow4 [1, 51, 441, 1795, 5073, 11571, 22921, 41091, 68385, 107443]
PolyRow5 [1, 188, 2955, 17422, 64469, 181776, 428863, 892130, 1689897, 2977444]
PolyRow6 [1, 731, 20805, 177463, 859385, 2994531, 8413021, 20305055, 43773873, 86483755]
PolyRow7 [1, 2950, 151695, 1870960, 11853949, 51038586, 170735515, 478070020, 1172900025, 2598372334]
PolyRow8 [1, 12235, 1135345, 20241403, 167763361, 892467691, 3554653585, 11546877595, 32238960193, 80081688331]
PolyRow9 [1, 51822, 8671763, 223438852, 2422342053, 15920944346, 75498599287, 284508841968, 903965284937, 2517734880838]

BinomialCatalan Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822]
PolyCol2 [1, 3, 13, 71, 441, 2955, 20805, 151695, 1135345, 8671763]
PolyCol3 [1, 4, 25, 199, 1795, 17422, 177463, 1870960, 20241403, 223438852]
PolyCol4 [1, 5, 41, 429, 5073, 64469, 859385, 11853949, 167763361, 2422342053]
PolyCol5 [1, 6, 61, 791, 11571, 181776, 2994531, 51038586, 892467691, 15920944346]
PolyCol6 [1, 7, 85, 1315, 22921, 428863, 8413021, 170735515, 3554653585, 75498599287]
PolyCol7 [1, 8, 113, 2031, 41091, 892130, 20305055, 478070020, 11546877595, 284508841968]
PolyCol8 [1, 9, 145, 2969, 68385, 1689897, 43773873, 1172900025, 32238960193, 903965284937]
PolyCol9 [1, 10, 181, 4159, 107443, 2977444, 86483755, 2598372334, 80081688331, 2517734880838]

BinomialCatalan:Rev

[]

BinomialCatalan:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 1]
Row2 [2, 2, 1]
Row3 [5, 6, 3, 1]
Row4 [14, 20, 12, 4, 1]
Row5 [42, 70, 50, 20, 5, 1]
Row6 [132, 252, 210, 100, 30, 6, 1]
Row7 [429, 924, 882, 490, 175, 42, 7, 1]
Row8 [1430, 3432, 3696, 2352, 980, 280, 56, 8, 1]
Row9 [4862, 12870, 15444, 11088, 5292, 1764, 420, 72, 9, 1]

BinomialCatalan:Rev Triangles

Flat Seq
Triangle [[1], [1, 1], [2, 2, 1], [5, 6, 3, 1], [14, 20, 12, 4, 1], [42, 70, 50, 20, 5, 1], [132, 252, 210, 100, 30, 6, 1], [429, 924, 882, 490, 175, 42, 7, 1], [1430, 3432, 3696, 2352, 980, 280, 56, 8, 1], [4862, 12870, 15444, 11088, 5292, 1764, 420, 72, 9, 1]]
RevTabl [[1], [1, 1], [1, 2, 2], [1, 3, 6, 5], [1, 4, 12, 20, 14], [1, 5, 20, 50, 70, 42], [1, 6, 30, 100, 210, 252, 132], [1, 7, 42, 175, 490, 882, 924, 429], [1, 8, 56, 280, 980, 2352, 3696, 3432, 1430], [1, 9, 72, 420, 1764, 5292, 11088, 15444, 12870, 4862]]
AntiDiag [[1], [1], [2, 1], [5, 2], [14, 6, 1], [42, 20, 3], [132, 70, 12, 1], [429, 252, 50, 4], [1430, 924, 210, 20, 1], [4862, 3432, 882, 100, 5]]
AccTabl [[1], [1, 2], [2, 4, 5], [5, 11, 14, 15], [14, 34, 46, 50, 51], [42, 112, 162, 182, 187, 188], [132, 384, 594, 694, 724, 730, 731], [429, 1353, 2235, 2725, 2900, 2942, 2949, 2950], [1430, 4862, 8558, 10910, 11890, 12170, 12226, 12234, 12235], [4862, 17732, 33176, 44264, 49556, 51320, 51740, 51812, 51821, 51822]]
RevAccTabl [[1], [2, 1], [5, 4, 2], [15, 14, 11, 5], [51, 50, 46, 34, 14], [188, 187, 182, 162, 112, 42], [731, 730, 724, 694, 594, 384, 132], [2950, 2949, 2942, 2900, 2725, 2235, 1353, 429], [12235, 12234, 12226, 12170, 11890, 10910, 8558, 4862, 1430], [51822, 51821, 51812, 51740, 51320, 49556, 44264, 33176, 17732, 4862]]
AccRevTabl [[1], [1, 2], [1, 3, 5], [1, 4, 10, 15], [1, 5, 17, 37, 51], [1, 6, 26, 76, 146, 188], [1, 7, 37, 137, 347, 599, 731], [1, 8, 50, 225, 715, 1597, 2521, 2950], [1, 9, 65, 345, 1325, 3677, 7373, 10805, 12235], [1, 10, 82, 502, 2266, 7558, 18646, 34090, 46960, 51822]]
DiffxTabl [[1], [1, 2], [2, 4, 3], [5, 12, 9, 4], [14, 40, 36, 16, 5], [42, 140, 150, 80, 25, 6], [132, 504, 630, 400, 150, 36, 7], [429, 1848, 2646, 1960, 875, 252, 49, 8], [1430, 6864, 11088, 9408, 4900, 1680, 392, 64, 9], [4862, 25740, 46332, 44352, 26460, 10584, 2940, 576, 81, 10]]

BinomialCatalan:Rev Row sums

Trait Seq
RowSum [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822]
EvenSum [1, 1, 3, 8, 27, 97, 373, 1493, 6163, 26027]
OddSum [0, 1, 2, 7, 24, 91, 358, 1457, 6072, 25795]
AltSum [1, 0, 1, 1, 3, 6, 15, 36, 91, 232]
AbsSum [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822]
AccSum [1, 3, 11, 45, 195, 873, 3989, 18483, 86515, 408105]
AccRevSum [1, 3, 9, 30, 111, 443, 1859, 8067, 35835, 161937]
DiagSum [1, 1, 3, 7, 21, 65, 215, 735, 2585, 9281]

BinomialCatalan:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 30, 420, 2100, 69300, 6306300, 1681680, 257297040]
RowGcd [1, 1, 2, 1, 2, 1, 2, 1, 2, 1]
RowMax [1, 1, 2, 6, 20, 70, 252, 924, 3696, 15444]
CentralE [1, 2, 12, 100, 980]
CentralO [1, 6, 50, 490, 5292]
ColMiddle [1, 1, 2, 6, 12, 50, 100, 490, 980, 5292]
ColLeft [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 2, 7, 33, 183, 1118, 7281, 49626, 349999, 2535078]
InvBinConv [1, 0, -1, 5, -9, -16, 185, -624, 175, 9080]
TransSqrs [0, 1, 6, 27, 120, 555, 2658, 13013, 64536, 322515]
TransNat0 [0, 1, 4, 15, 60, 255, 1128, 5117, 23600, 110115]
TransNat1 [1, 3, 9, 30, 111, 443, 1859, 8067, 35835, 161937]
PosHalf [1, 3, 13, 71, 441, 2955, 20805, 151695, 1135345, 8671763]
NegHalf [1, -1, 5, -21, 105, -553, 3053, -17405, 101713, -606033]

BinomialCatalan:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
DiagRow2 [2, 6, 12, 20, 30, 42, 56, 72, 90, 110]
DiagRow3 [5, 20, 50, 100, 175, 280, 420, 600, 825, 1100]
DiagRow4 [14, 70, 210, 490, 980, 1764, 2940, 4620, 6930, 10010]
DiagRow5 [42, 252, 882, 2352, 5292, 10584, 19404, 33264, 54054, 84084]
DiagRow6 [132, 924, 3696, 11088, 27720, 60984, 121968, 226512, 396396, 660660]
DiagRow7 [429, 3432, 15444, 51480, 141570, 339768, 736164, 1472328, 2760615, 4907760]
DiagRow8 [1430, 12870, 64350, 235950, 707850, 1840410, 4294290, 9202050, 18404100, 34763300]
DiagRow9 [4862, 48620, 267410, 1069640, 3476330, 9733724, 24334310, 55621280, 118195220, 236390440]

BinomialCatalan:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]
DiagCol1 [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620]
DiagCol2 [1, 3, 12, 50, 210, 882, 3696, 15444, 64350, 267410]
DiagCol3 [1, 4, 20, 100, 490, 2352, 11088, 51480, 235950, 1069640]
DiagCol4 [1, 5, 30, 175, 980, 5292, 27720, 141570, 707850, 3476330]
DiagCol5 [1, 6, 42, 280, 1764, 10584, 60984, 339768, 1840410, 9733724]
DiagCol6 [1, 7, 56, 420, 2940, 19404, 121968, 736164, 4294290, 24334310]
DiagCol7 [1, 8, 72, 600, 4620, 33264, 226512, 1472328, 9202050, 55621280]
DiagCol8 [1, 9, 90, 825, 6930, 54054, 396396, 2760615, 18404100, 118195220]
DiagCol9 [1, 10, 110, 1100, 10010, 84084, 660660, 4907760, 34763300, 236390440]

BinomialCatalan: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 [2, 5, 10, 17, 26, 37, 50, 65, 82, 101]
PolyRow3 [5, 15, 37, 77, 141, 235, 365, 537, 757, 1031]
PolyRow4 [14, 51, 150, 371, 798, 1539, 2726, 4515, 7086, 10643]
PolyRow5 [42, 188, 654, 1890, 4706, 10392, 20838, 38654, 67290, 111156]
PolyRow6 [132, 731, 3012, 10095, 28820, 72267, 162996, 337007, 648420, 1174875]
PolyRow7 [429, 2950, 14445, 56040, 182461, 516474, 1303485, 2991340, 6340365, 12568686]
PolyRow8 [1430, 12235, 71398, 320795, 1188406, 3783115, 10642310, 27013723, 62893270, 136080971]
PolyRow9 [4862, 51822, 361114, 1881524, 7926102, 28317562, 88553522, 247953024, 632560174, 1490758022]

BinomialCatalan:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]
PolyCol1 [1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822]
PolyCol2 [1, 3, 10, 37, 150, 654, 3012, 14445, 71398, 361114]
PolyCol3 [1, 4, 17, 77, 371, 1890, 10095, 56040, 320795, 1881524]
PolyCol4 [1, 5, 26, 141, 798, 4706, 28820, 182461, 1188406, 7926102]
PolyCol5 [1, 6, 37, 235, 1539, 10392, 72267, 516474, 3783115, 28317562]
PolyCol6 [1, 7, 50, 365, 2726, 20838, 162996, 1303485, 10642310, 88553522]
PolyCol7 [1, 8, 65, 537, 4515, 38654, 337007, 2991340, 27013723, 247953024]
PolyCol8 [1, 9, 82, 757, 7086, 67290, 648420, 6340365, 62893270, 632560174]
PolyCol9 [1, 10, 101, 1031, 10643, 111156, 1174875, 12568686, 136080971, 1490758022]

BinomialCatalan:Rev:Inv

[]

BinomialCatalan:Rev:Inv Triangle view

Row Seq
Row0 [1]
Row1 [-1, 1]
Row2 [0, -2, 1]
Row3 [1, 0, -3, 1]
Row4 [2, 4, 0, -4, 1]
Row5 [-2, 10, 10, 0, -5, 1]
Row6 [-28, -12, 30, 20, 0, -6, 1]
Row7 [-65, -196, -42, 70, 35, 0, -7, 1]
Row8 [338, -520, -784, -112, 140, 56, 0, -8, 1]
Row9 [3262, 3042, -2340, -2352, -252, 252, 84, 0, -9, 1]

BinomialCatalan:Rev:Inv Triangles

Flat Seq
Triangle [[1], [-1, 1], [0, -2, 1], [1, 0, -3, 1], [2, 4, 0, -4, 1], [-2, 10, 10, 0, -5, 1], [-28, -12, 30, 20, 0, -6, 1], [-65, -196, -42, 70, 35, 0, -7, 1], [338, -520, -784, -112, 140, 56, 0, -8, 1], [3262, 3042, -2340, -2352, -252, 252, 84, 0, -9, 1]]
RevTabl [[1], [1, -1], [1, -2, 0], [1, -3, 0, 1], [1, -4, 0, 4, 2], [1, -5, 0, 10, 10, -2], [1, -6, 0, 20, 30, -12, -28], [1, -7, 0, 35, 70, -42, -196, -65], [1, -8, 0, 56, 140, -112, -784, -520, 338], [1, -9, 0, 84, 252, -252, -2352, -2340, 3042, 3262]]
AntiDiag [[1], [-1], [0, 1], [1, -2], [2, 0, 1], [-2, 4, -3], [-28, 10, 0, 1], [-65, -12, 10, -4], [338, -196, 30, 0, 1], [3262, -520, -42, 20, -5]]
AccTabl [[1], [-1, 0], [0, -2, -1], [1, 1, -2, -1], [2, 6, 6, 2, 3], [-2, 8, 18, 18, 13, 14], [-28, -40, -10, 10, 10, 4, 5], [-65, -261, -303, -233, -198, -198, -205, -204], [338, -182, -966, -1078, -938, -882, -882, -890, -889], [3262, 6304, 3964, 1612, 1360, 1612, 1696, 1696, 1687, 1688]]
RevAccTabl [[1], [0, -1], [-1, -2, 0], [-1, -2, 1, 1], [3, 2, 6, 6, 2], [14, 13, 18, 18, 8, -2], [5, 4, 10, 10, -10, -40, -28], [-204, -205, -198, -198, -233, -303, -261, -65], [-889, -890, -882, -882, -938, -1078, -966, -182, 338], [1688, 1687, 1696, 1696, 1612, 1360, 1612, 3964, 6304, 3262]]
AccRevTabl [[1], [1, 0], [1, -1, -1], [1, -2, -2, -1], [1, -3, -3, 1, 3], [1, -4, -4, 6, 16, 14], [1, -5, -5, 15, 45, 33, 5], [1, -6, -6, 29, 99, 57, -139, -204], [1, -7, -7, 49, 189, 77, -707, -1227, -889], [1, -8, -8, 76, 328, 76, -2276, -4616, -1574, 1688]]
DiffxTabl [[1], [-1, 2], [0, -4, 3], [1, 0, -9, 4], [2, 8, 0, -16, 5], [-2, 20, 30, 0, -25, 6], [-28, -24, 90, 80, 0, -36, 7], [-65, -392, -126, 280, 175, 0, -49, 8], [338, -1040, -2352, -448, 700, 336, 0, -64, 9], [3262, 6084, -7020, -9408, -1260, 1512, 588, 0, -81, 10]]

BinomialCatalan:Rev:Inv Row sums

Trait Seq
RowSum [1, 0, -1, -1, 3, 14, 5, -204, -889, 1688]
EvenSum [1, -1, 1, -2, 3, 3, 3, -79, -305, 745]
OddSum [0, 1, -2, 1, 0, 11, 2, -125, -584, 943]
AltSum [1, -2, 3, -3, 3, -8, 1, 46, 279, -198]
AbsSum [1, 2, 3, 5, 11, 28, 97, 416, 1959, 11594]
AccSum [1, -1, -3, -1, 19, 69, -49, -1667, -6369, 24881]
AccRevSum [1, 1, -1, -4, -1, 29, 89, -169, -2521, -6313]
DiagSum [1, -1, 1, -1, 3, -1, -17, -71, 173, 2715]

BinomialCatalan:Rev:Inv Transforms

Trans Seq
RowLcm [1, 1, 2, 3, 4, 10, 420, 38220, 662480, 1389220560]
RowGcd [1, 1, 2, 3, 2, 1, 2, 1, 2, 1]
RowMax [1, 1, 2, 3, 4, 10, 30, 196, 784, 3262]
CentralE [1, -2, 0, 20, 140]
CentralO [-1, 0, 10, 70, -252]
ColMiddle [1, -1, -2, 0, 0, 10, 20, 70, 140, -252]
ColLeft [1, -1, 0, 1, 2, -2, -28, -65, 338, 3262]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 0, -3, -7, 3, 124, 715, 1308, -19173, -244192]
InvBinConv [1, 2, 5, 9, 3, -22, 131, 850, -4453, -32682]
TransSqrs [0, 1, 2, -3, -16, -5, 174, 623, -1352, -22689]
TransNat0 [0, 1, 0, -3, -4, 15, 84, 35, -1632, -8001]
TransNat1 [1, 1, -1, -4, -1, 29, 89, -169, -2521, -6313]
PosHalf [1, -1, -3, 3, 57, 167, -1547, -20821, -31119, 1995471]
NegHalf [1, 3, 5, -1, 9, 155, -1075, -2025, 108305, -730957]

BinomialCatalan:Rev:Inv Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]
DiagRow2 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow3 [1, 4, 10, 20, 35, 56, 84, 120, 165, 220]
DiagRow4 [2, 10, 30, 70, 140, 252, 420, 660, 990, 1430]
DiagRow5 [-2, -12, -42, -112, -252, -504, -924, -1584, -2574, -4004]
DiagRow6 [-28, -196, -784, -2352, -5880, -12936, -25872, -48048, -84084, -140140]
DiagRow7 [-65, -520, -2340, -7800, -21450, -51480, -111540, -223080, -418275, -743600]
DiagRow8 [338, 3042, 15210, 55770, 167310, 435006, 1015014, 2175030, 4350060, 8216780]
DiagRow9 [3262, 32620, 179410, 717640, 2332330, 6530524, 16326310, 37317280, 79299220, 158598440]

BinomialCatalan:Rev:Inv Diagonals as columns

DiagCol Seq
DiagCol0 [1, -1, 0, 1, 2, -2, -28, -65, 338, 3262]
DiagCol1 [1, -2, 0, 4, 10, -12, -196, -520, 3042, 32620]
DiagCol2 [1, -3, 0, 10, 30, -42, -784, -2340, 15210, 179410]
DiagCol3 [1, -4, 0, 20, 70, -112, -2352, -7800, 55770, 717640]
DiagCol4 [1, -5, 0, 35, 140, -252, -5880, -21450, 167310, 2332330]
DiagCol5 [1, -6, 0, 56, 252, -504, -12936, -51480, 435006, 6530524]
DiagCol6 [1, -7, 0, 84, 420, -924, -25872, -111540, 1015014, 16326310]
DiagCol7 [1, -8, 0, 120, 660, -1584, -48048, -223080, 2175030, 37317280]
DiagCol8 [1, -9, 0, 165, 990, -2574, -84084, -418275, 4350060, 79299220]
DiagCol9 [1, -10, 0, 220, 1430, -4004, -140140, -743600, 8216780, 158598440]

BinomialCatalan:Rev: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 [0, -1, 0, 3, 8, 15, 24, 35, 48, 63]
PolyRow3 [1, -1, -3, 1, 17, 51, 109, 197, 321, 487]
PolyRow4 [2, 3, -6, -13, 18, 147, 458, 1059, 2082, 3683]
PolyRow5 [-2, 14, 10, -44, -58, 298, 1714, 5360, 13006, 27142]
PolyRow6 [-28, 5, 100, 17, -364, 37, 5300, 25025, 77572, 194021]
PolyRow7 [-65, -204, 175, 778, -369, -2720, 11071, 104550, 437023, 1338316]
PolyRow8 [338, -889, -1470, 2711, 6194, -7737, 1826, 373655, 2297106, 8858759]
PolyRow9 [3262, 1688, -11214, -9482, 37382, 45972, -57542, 1086386, 11141838, 55994512]

BinomialCatalan:Rev:Inv Polynomial values as columns

PolyCol Seq
PolyCol0 [1, -1, 0, 1, 2, -2, -28, -65, 338, 3262]
PolyCol1 [1, 0, -1, -1, 3, 14, 5, -204, -889, 1688]
PolyCol2 [1, 1, 0, -3, -6, 10, 100, 175, -1470, -11214]
PolyCol3 [1, 2, 3, 1, -13, -44, 17, 778, 2711, -9482]
PolyCol4 [1, 3, 8, 17, 18, -58, -364, -369, 6194, 37382]
PolyCol5 [1, 4, 15, 51, 147, 298, 37, -2720, -7737, 45972]
PolyCol6 [1, 5, 24, 109, 458, 1714, 5300, 11071, 1826, -57542]
PolyCol7 [1, 6, 35, 197, 1059, 5360, 25025, 104550, 373655, 1086386]
PolyCol8 [1, 7, 48, 321, 2082, 13006, 77572, 437023, 2297106, 11141838]
PolyCol9 [1, 8, 63, 487, 3683, 27142, 194021, 1338316, 8858759, 55994512]