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Lah

['A271703', 'A008297', 'A066667', 'A089231', 'A105278', 'A111596']

Lah Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, 2, 1]
Row3 [0, 6, 6, 1]
Row4 [0, 24, 36, 12, 1]
Row5 [0, 120, 240, 120, 20, 1]
Row6 [0, 720, 1800, 1200, 300, 30, 1]
Row7 [0, 5040, 15120, 12600, 4200, 630, 42, 1]
Row8 [0, 40320, 141120, 141120, 58800, 11760, 1176, 56, 1]
Row9 [0, 362880, 1451520, 1693440, 846720, 211680, 28224, 2016, 72, 1]

Lah Triangles

Flat Seq
Triangle [[1], [0, 1], [0, 2, 1], [0, 6, 6, 1], [0, 24, 36, 12, 1], [0, 120, 240, 120, 20, 1], [0, 720, 1800, 1200, 300, 30, 1], [0, 5040, 15120, 12600, 4200, 630, 42, 1], [0, 40320, 141120, 141120, 58800, 11760, 1176, 56, 1], [0, 362880, 1451520, 1693440, 846720, 211680, 28224, 2016, 72, 1]]
RevTabl [[1], [1, 0], [1, 2, 0], [1, 6, 6, 0], [1, 12, 36, 24, 0], [1, 20, 120, 240, 120, 0], [1, 30, 300, 1200, 1800, 720, 0], [1, 42, 630, 4200, 12600, 15120, 5040, 0], [1, 56, 1176, 11760, 58800, 141120, 141120, 40320, 0], [1, 72, 2016, 28224, 211680, 846720, 1693440, 1451520, 362880, 0]]
AntiDiag [[1], [0], [0, 1], [0, 2], [0, 6, 1], [0, 24, 6], [0, 120, 36, 1], [0, 720, 240, 12], [0, 5040, 1800, 120, 1], [0, 40320, 15120, 1200, 20]]
AccTabl [[1], [0, 1], [0, 2, 3], [0, 6, 12, 13], [0, 24, 60, 72, 73], [0, 120, 360, 480, 500, 501], [0, 720, 2520, 3720, 4020, 4050, 4051], [0, 5040, 20160, 32760, 36960, 37590, 37632, 37633], [0, 40320, 181440, 322560, 381360, 393120, 394296, 394352, 394353], [0, 362880, 1814400, 3507840, 4354560, 4566240, 4594464, 4596480, 4596552, 4596553]]
RevAccTabl [[1], [1, 0], [3, 2, 0], [13, 12, 6, 0], [73, 72, 60, 24, 0], [501, 500, 480, 360, 120, 0], [4051, 4050, 4020, 3720, 2520, 720, 0], [37633, 37632, 37590, 36960, 32760, 20160, 5040, 0], [394353, 394352, 394296, 393120, 381360, 322560, 181440, 40320, 0], [4596553, 4596552, 4596480, 4594464, 4566240, 4354560, 3507840, 1814400, 362880, 0]]
AccRevTabl [[1], [1, 1], [1, 3, 3], [1, 7, 13, 13], [1, 13, 49, 73, 73], [1, 21, 141, 381, 501, 501], [1, 31, 331, 1531, 3331, 4051, 4051], [1, 43, 673, 4873, 17473, 32593, 37633, 37633], [1, 57, 1233, 12993, 71793, 212913, 354033, 394353, 394353], [1, 73, 2089, 30313, 241993, 1088713, 2782153, 4233673, 4596553, 4596553]]
DiffxTabl [[1], [0, 2], [0, 4, 3], [0, 12, 18, 4], [0, 48, 108, 48, 5], [0, 240, 720, 480, 100, 6], [0, 1440, 5400, 4800, 1500, 180, 7], [0, 10080, 45360, 50400, 21000, 3780, 294, 8], [0, 80640, 423360, 564480, 294000, 70560, 8232, 448, 9], [0, 725760, 4354560, 6773760, 4233600, 1270080, 197568, 16128, 648, 10]]

Lah Row sums

Trait Seq
RowSum [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
EvenSum [1, 0, 1, 6, 37, 260, 2101, 19362, 201097, 2326536]
OddSum [0, 1, 2, 7, 36, 241, 1950, 18271, 193256, 2270017]
AltSum [1, -1, -1, -1, 1, 19, 151, 1091, 7841, 56519]
AbsSum [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
AccSum [1, 1, 5, 31, 229, 1961, 19081, 207775, 2501801, 32989969]
AccRevSum [1, 2, 7, 34, 209, 1546, 13327, 130922, 1441729, 17572114]
DiagSum [1, 0, 1, 2, 7, 30, 157, 972, 6961, 56660]

Lah Transforms

Trans Seq
RowLcm [1, 1, 2, 6, 72, 240, 3600, 75600, 1411200, 10160640]
RowGcd [1, 1, 2, 6, 12, 20, 30, 42, 56, 72]
RowMax [1, 1, 2, 6, 36, 240, 1800, 15120, 141120, 1693440]
CentralE [1, 2, 36, 1200, 58800]
CentralO [0, 6, 240, 12600, 846720]
ColMiddle [1, 0, 2, 6, 36, 240, 1200, 12600, 58800, 846720]
ColLeft [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 1, 5, 37, 361, 4301, 60001, 954325, 16984577, 333572041]
InvBinConv [1, 1, -3, 1, 73, -699, 3001, 24697, -783999, 10946233]
TransSqrs [0, 1, 6, 39, 292, 2505, 24306, 263431, 3154824, 41368977]
TransNat0 [0, 1, 4, 21, 136, 1045, 9276, 93289, 1047376, 12975561]
TransNat1 [1, 2, 7, 34, 209, 1546, 13327, 130922, 1441729, 17572114]
PosHalf [1, 1, 5, 37, 361, 4361, 62701, 1044205, 19748177, 417787921]
NegHalf [1, 1, -3, 13, -71, 441, -2699, 9157, 206193, -8443151]

Lah Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, 2, 6, 12, 20, 30, 42, 56, 72, 90]
DiagRow2 [0, 6, 36, 120, 300, 630, 1176, 2016, 3240, 4950]
DiagRow3 [0, 24, 240, 1200, 4200, 11760, 28224, 60480, 118800, 217800]
DiagRow4 [0, 120, 1800, 12600, 58800, 211680, 635040, 1663200, 3920400, 8494200]
DiagRow5 [0, 720, 15120, 141120, 846720, 3810240, 13970880, 43908480, 122316480, 309188880]
DiagRow6 [0, 5040, 141120, 1693440, 12700800, 69854400, 307359360, 1141620480, 3710266560, 10821610800]
DiagRow7 [0, 40320, 1451520, 21772800, 199584000, 1317254400, 6849722880, 29682132480, 111307996800, 371026656000]
DiagRow8 [0, 362880, 16329600, 299376000, 3293136000, 25686460800, 155831195520, 779155977600, 3339239904000, 12614906304000]
DiagRow9 [0, 3628800, 199584000, 4390848000, 57081024000, 519437318400, 3636061228800, 20777492736000, 100919250432000, 428906814336000]

Lah Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
DiagCol2 [1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600, 199584000]
DiagCol3 [1, 12, 120, 1200, 12600, 141120, 1693440, 21772800, 299376000, 4390848000]
DiagCol4 [1, 20, 300, 4200, 58800, 846720, 12700800, 199584000, 3293136000, 57081024000]
DiagCol5 [1, 30, 630, 11760, 211680, 3810240, 69854400, 1317254400, 25686460800, 519437318400]
DiagCol6 [1, 42, 1176, 28224, 635040, 13970880, 307359360, 6849722880, 155831195520, 3636061228800]
DiagCol7 [1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480, 779155977600, 20777492736000]
DiagCol8 [1, 72, 3240, 118800, 3920400, 122316480, 3710266560, 111307996800, 3339239904000, 100919250432000]
DiagCol9 [1, 90, 4950, 217800, 8494200, 309188880, 10821610800, 371026656000, 12614906304000, 428906814336000]

Lah Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2 [0, 3, 8, 15, 24, 35, 48, 63, 80, 99]
PolyRow3 [0, 13, 44, 99, 184, 305, 468, 679, 944, 1269]
PolyRow4 [0, 73, 304, 801, 1696, 3145, 5328, 8449, 12736, 18441]
PolyRow5 [0, 501, 2512, 7623, 18144, 37225, 68976, 118587, 192448, 298269]
PolyRow6 [0, 4051, 24064, 83079, 220096, 495475, 997056, 1846999, 3209344, 5298291]
PolyRow7 [0, 37633, 261536, 1017495, 2977216, 7306325, 15877728, 31535371, 58413440, 102316041]
PolyRow8 [0, 394353, 3173888, 13808097, 44345856, 118010225, 275678208, 584668833, 1150303232, 2130740721]
PolyRow9 [0, 4596553, 42483968, 205374123, 720193024, 2069060525, 5175767808, 11681402383, 24336124928, 47538819729]

Lah Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
PolyCol2 [1, 2, 8, 44, 304, 2512, 24064, 261536, 3173888, 42483968]
PolyCol3 [1, 3, 15, 99, 801, 7623, 83079, 1017495, 13808097, 205374123]
PolyCol4 [1, 4, 24, 184, 1696, 18144, 220096, 2977216, 44345856, 720193024]
PolyCol5 [1, 5, 35, 305, 3145, 37225, 495475, 7306325, 118010225, 2069060525]
PolyCol6 [1, 6, 48, 468, 5328, 68976, 997056, 15877728, 275678208, 5175767808]
PolyCol7 [1, 7, 63, 679, 8449, 118587, 1846999, 31535371, 584668833, 11681402383]
PolyCol8 [1, 8, 80, 944, 12736, 192448, 3209344, 58413440, 1150303232, 24336124928]
PolyCol9 [1, 9, 99, 1269, 18441, 298269, 5298291, 102316041, 2130740721, 47538819729]

Lah:Inv

[]

Lah:Inv Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, -2, 1]
Row3 [0, 6, -6, 1]
Row4 [0, -24, 36, -12, 1]
Row5 [0, 120, -240, 120, -20, 1]
Row6 [0, -720, 1800, -1200, 300, -30, 1]
Row7 [0, 5040, -15120, 12600, -4200, 630, -42, 1]
Row8 [0, -40320, 141120, -141120, 58800, -11760, 1176, -56, 1]
Row9 [0, 362880, -1451520, 1693440, -846720, 211680, -28224, 2016, -72, 1]

Lah:Inv Triangles

Flat Seq
Triangle [[1], [0, 1], [0, -2, 1], [0, 6, -6, 1], [0, -24, 36, -12, 1], [0, 120, -240, 120, -20, 1], [0, -720, 1800, -1200, 300, -30, 1], [0, 5040, -15120, 12600, -4200, 630, -42, 1], [0, -40320, 141120, -141120, 58800, -11760, 1176, -56, 1], [0, 362880, -1451520, 1693440, -846720, 211680, -28224, 2016, -72, 1]]
RevTabl [[1], [1, 0], [1, -2, 0], [1, -6, 6, 0], [1, -12, 36, -24, 0], [1, -20, 120, -240, 120, 0], [1, -30, 300, -1200, 1800, -720, 0], [1, -42, 630, -4200, 12600, -15120, 5040, 0], [1, -56, 1176, -11760, 58800, -141120, 141120, -40320, 0], [1, -72, 2016, -28224, 211680, -846720, 1693440, -1451520, 362880, 0]]
AntiDiag [[1], [0], [0, 1], [0, -2], [0, 6, 1], [0, -24, -6], [0, 120, 36, 1], [0, -720, -240, -12], [0, 5040, 1800, 120, 1], [0, -40320, -15120, -1200, -20]]
AccTabl [[1], [0, 1], [0, -2, -1], [0, 6, 0, 1], [0, -24, 12, 0, 1], [0, 120, -120, 0, -20, -19], [0, -720, 1080, -120, 180, 150, 151], [0, 5040, -10080, 2520, -1680, -1050, -1092, -1091], [0, -40320, 100800, -40320, 18480, 6720, 7896, 7840, 7841], [0, 362880, -1088640, 604800, -241920, -30240, -58464, -56448, -56520, -56519]]
RevAccTabl [[1], [1, 0], [-1, -2, 0], [1, 0, 6, 0], [1, 0, 12, -24, 0], [-19, -20, 0, -120, 120, 0], [151, 150, 180, -120, 1080, -720, 0], [-1091, -1092, -1050, -1680, 2520, -10080, 5040, 0], [7841, 7840, 7896, 6720, 18480, -40320, 100800, -40320, 0], [-56519, -56520, -56448, -58464, -30240, -241920, 604800, -1088640, 362880, 0]]
AccRevTabl [[1], [1, 1], [1, -1, -1], [1, -5, 1, 1], [1, -11, 25, 1, 1], [1, -19, 101, -139, -19, -19], [1, -29, 271, -929, 871, 151, 151], [1, -41, 589, -3611, 8989, -6131, -1091, -1091], [1, -55, 1121, -10639, 48161, -92959, 48161, 7841, 7841], [1, -71, 1945, -26279, 185401, -661319, 1032121, -419399, -56519, -56519]]
DiffxTabl [[1], [0, 2], [0, -4, 3], [0, 12, -18, 4], [0, -48, 108, -48, 5], [0, 240, -720, 480, -100, 6], [0, -1440, 5400, -4800, 1500, -180, 7], [0, 10080, -45360, 50400, -21000, 3780, -294, 8], [0, -80640, 423360, -564480, 294000, -70560, 8232, -448, 9], [0, 725760, -4354560, 6773760, -4233600, 1270080, -197568, 16128, -648, 10]]

Lah:Inv Row sums

Trait Seq
RowSum [1, 1, -1, 1, 1, -19, 151, -1091, 7841, -56519]
EvenSum [1, 0, 1, -6, 37, -260, 2101, -19362, 201097, -2326536]
OddSum [0, 1, -2, 7, -36, 241, -1950, 18271, -193256, 2270017]
AltSum [1, -1, 3, -13, 73, -501, 4051, -37633, 394353, -4596553]
AbsSum [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
AccSum [1, 1, -3, 7, -11, -39, 721, -7433, 68937, -621071]
AccRevSum [1, 2, -1, -2, 17, -94, 487, -2386, 9473, -638]
DiagSum [1, 0, 1, -2, 7, -30, 157, -972, 6961, -56660]

Lah:Inv Transforms

Trans Seq
RowLcm [1, 1, 2, 6, 72, 240, 3600, 75600, 1411200, 10160640]
RowGcd [1, 1, 2, 6, 12, 20, 30, 42, 56, 72]
RowMax [1, 1, 2, 6, 36, 240, 1800, 15120, 141120, 1693440]
CentralE [1, -2, 36, -1200, 58800]
CentralO [0, 6, -240, 12600, -846720]
ColMiddle [1, 0, -2, 6, 36, -240, -1200, 12600, 58800, -846720]
ColLeft [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 1, -3, 1, 73, -699, 3001, 24697, -783999, 10946233]
InvBinConv [1, 1, 5, 37, 361, 4301, 60001, 954325, 16984577, 333572041]
TransSqrs [0, 1, 2, -9, 28, -55, -234, 5047, -59464, 620433]
TransNat0 [0, 1, 0, -3, 16, -75, 336, -1295, 1632, 55881]
TransNat1 [1, 2, -1, -2, 17, -94, 487, -2386, 9473, -638]
PosHalf [1, 1, -3, 13, -71, 441, -2699, 9157, 206193, -8443151]
NegHalf [1, 1, 5, 37, 361, 4361, 62701, 1044205, 19748177, 417787921]

Lah:Inv Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, -2, -6, -12, -20, -30, -42, -56, -72, -90]
DiagRow2 [0, 6, 36, 120, 300, 630, 1176, 2016, 3240, 4950]
DiagRow3 [0, -24, -240, -1200, -4200, -11760, -28224, -60480, -118800, -217800]
DiagRow4 [0, 120, 1800, 12600, 58800, 211680, 635040, 1663200, 3920400, 8494200]
DiagRow5 [0, -720, -15120, -141120, -846720, -3810240, -13970880, -43908480, -122316480, -309188880]
DiagRow6 [0, 5040, 141120, 1693440, 12700800, 69854400, 307359360, 1141620480, 3710266560, 10821610800]
DiagRow7 [0, -40320, -1451520, -21772800, -199584000, -1317254400, -6849722880, -29682132480, -111307996800, -371026656000]
DiagRow8 [0, 362880, 16329600, 299376000, 3293136000, 25686460800, 155831195520, 779155977600, 3339239904000, 12614906304000]
DiagRow9 [0, -3628800, -199584000, -4390848000, -57081024000, -519437318400, -3636061228800, -20777492736000, -100919250432000, -428906814336000]

Lah:Inv Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, -2, 6, -24, 120, -720, 5040, -40320, 362880, -3628800]
DiagCol2 [1, -6, 36, -240, 1800, -15120, 141120, -1451520, 16329600, -199584000]
DiagCol3 [1, -12, 120, -1200, 12600, -141120, 1693440, -21772800, 299376000, -4390848000]
DiagCol4 [1, -20, 300, -4200, 58800, -846720, 12700800, -199584000, 3293136000, -57081024000]
DiagCol5 [1, -30, 630, -11760, 211680, -3810240, 69854400, -1317254400, 25686460800, -519437318400]
DiagCol6 [1, -42, 1176, -28224, 635040, -13970880, 307359360, -6849722880, 155831195520, -3636061228800]
DiagCol7 [1, -56, 2016, -60480, 1663200, -43908480, 1141620480, -29682132480, 779155977600, -20777492736000]
DiagCol8 [1, -72, 3240, -118800, 3920400, -122316480, 3710266560, -111307996800, 3339239904000, -100919250432000]
DiagCol9 [1, -90, 4950, -217800, 8494200, -309188880, 10821610800, -371026656000, 12614906304000, -428906814336000]

Lah:Inv Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2 [0, -1, 0, 3, 8, 15, 24, 35, 48, 63]
PolyRow3 [0, 1, -4, -9, -8, 5, 36, 91, 176, 297]
PolyRow4 [0, 1, 16, 9, -32, -95, -144, -119, 64, 513]
PolyRow5 [0, -19, -48, 63, 224, 225, -144, -973, -2112, -3051]
PolyRow6 [0, 151, 64, -621, -704, 775, 3456, 5299, 2944, -7209]
PolyRow7 [0, -1091, 800, 3699, -1088, -12175, -16416, 2695, 51584, 113157]
PolyRow8 [0, 7841, -12288, -14607, 40448, 77025, -13824, -241423, -433152, -263007]
PolyRow9 [0, -56519, 127232, -17253, -424448, -165475, 1057536, 2021887, 576512, -4495743]

Lah:Inv Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, -1, 1, 1, -19, 151, -1091, 7841, -56519]
PolyCol2 [1, 2, 0, -4, 16, -48, 64, 800, -12288, 127232]
PolyCol3 [1, 3, 3, -9, 9, 63, -621, 3699, -14607, -17253]
PolyCol4 [1, 4, 8, -8, -32, 224, -704, -1088, 40448, -424448]
PolyCol5 [1, 5, 15, 5, -95, 225, 775, -12175, 77025, -165475]
PolyCol6 [1, 6, 24, 36, -144, -144, 3456, -16416, -13824, 1057536]
PolyCol7 [1, 7, 35, 91, -119, -973, 5299, 2695, -241423, 2021887]
PolyCol8 [1, 8, 48, 176, 64, -2112, 2944, 51584, -433152, 576512]
PolyCol9 [1, 9, 63, 297, 513, -3051, -7209, 113157, -263007, -4495743]

Lah:Rev

[]

Lah:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, 2, 0]
Row3 [1, 6, 6, 0]
Row4 [1, 12, 36, 24, 0]
Row5 [1, 20, 120, 240, 120, 0]
Row6 [1, 30, 300, 1200, 1800, 720, 0]
Row7 [1, 42, 630, 4200, 12600, 15120, 5040, 0]
Row8 [1, 56, 1176, 11760, 58800, 141120, 141120, 40320, 0]
Row9 [1, 72, 2016, 28224, 211680, 846720, 1693440, 1451520, 362880, 0]

Lah:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, 2, 0], [1, 6, 6, 0], [1, 12, 36, 24, 0], [1, 20, 120, 240, 120, 0], [1, 30, 300, 1200, 1800, 720, 0], [1, 42, 630, 4200, 12600, 15120, 5040, 0], [1, 56, 1176, 11760, 58800, 141120, 141120, 40320, 0], [1, 72, 2016, 28224, 211680, 846720, 1693440, 1451520, 362880, 0]]
RevTabl [[1], [0, 1], [0, 2, 1], [0, 6, 6, 1], [0, 24, 36, 12, 1], [0, 120, 240, 120, 20, 1], [0, 720, 1800, 1200, 300, 30, 1], [0, 5040, 15120, 12600, 4200, 630, 42, 1], [0, 40320, 141120, 141120, 58800, 11760, 1176, 56, 1], [0, 362880, 1451520, 1693440, 846720, 211680, 28224, 2016, 72, 1]]
AntiDiag [[1], [1], [1, 0], [1, 2], [1, 6, 0], [1, 12, 6], [1, 20, 36, 0], [1, 30, 120, 24], [1, 42, 300, 240, 0], [1, 56, 630, 1200, 120]]
AccTabl [[1], [1, 1], [1, 3, 3], [1, 7, 13, 13], [1, 13, 49, 73, 73], [1, 21, 141, 381, 501, 501], [1, 31, 331, 1531, 3331, 4051, 4051], [1, 43, 673, 4873, 17473, 32593, 37633, 37633], [1, 57, 1233, 12993, 71793, 212913, 354033, 394353, 394353], [1, 73, 2089, 30313, 241993, 1088713, 2782153, 4233673, 4596553, 4596553]]
RevAccTabl [[1], [1, 1], [3, 3, 1], [13, 13, 7, 1], [73, 73, 49, 13, 1], [501, 501, 381, 141, 21, 1], [4051, 4051, 3331, 1531, 331, 31, 1], [37633, 37633, 32593, 17473, 4873, 673, 43, 1], [394353, 394353, 354033, 212913, 71793, 12993, 1233, 57, 1], [4596553, 4596553, 4233673, 2782153, 1088713, 241993, 30313, 2089, 73, 1]]
AccRevTabl [[1], [0, 1], [0, 2, 3], [0, 6, 12, 13], [0, 24, 60, 72, 73], [0, 120, 360, 480, 500, 501], [0, 720, 2520, 3720, 4020, 4050, 4051], [0, 5040, 20160, 32760, 36960, 37590, 37632, 37633], [0, 40320, 181440, 322560, 381360, 393120, 394296, 394352, 394353], [0, 362880, 1814400, 3507840, 4354560, 4566240, 4594464, 4596480, 4596552, 4596553]]
DiffxTabl [[1], [1, 0], [1, 4, 0], [1, 12, 18, 0], [1, 24, 108, 96, 0], [1, 40, 360, 960, 600, 0], [1, 60, 900, 4800, 9000, 4320, 0], [1, 84, 1890, 16800, 63000, 90720, 35280, 0], [1, 112, 3528, 47040, 294000, 846720, 987840, 322560, 0], [1, 144, 6048, 112896, 1058400, 5080320, 11854080, 11612160, 3265920, 0]]

Lah:Rev Row sums

Trait Seq
RowSum [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
EvenSum [1, 1, 1, 7, 37, 241, 2101, 18271, 201097, 2270017]
OddSum [0, 0, 2, 6, 36, 260, 1950, 19362, 193256, 2326536]
AltSum [1, 1, -1, 1, 1, -19, 151, -1091, 7841, -56519]
AbsSum [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
AccSum [1, 2, 7, 34, 209, 1546, 13327, 130922, 1441729, 17572114]
AccRevSum [1, 1, 5, 31, 229, 1961, 19081, 207775, 2501801, 32989969]
DiagSum [1, 1, 1, 3, 7, 19, 57, 175, 583, 2007]

Lah:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 6, 72, 240, 3600, 75600, 1411200, 10160640]
RowGcd [1, 1, 2, 6, 12, 20, 30, 42, 56, 72]
RowMax [1, 1, 2, 6, 36, 240, 1800, 15120, 141120, 1693440]
CentralE [1, 2, 36, 1200, 58800]
CentralO [1, 6, 120, 4200, 211680]
ColMiddle [1, 1, 2, 6, 36, 120, 1200, 4200, 58800, 211680]
ColLeft [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [1, 1, 5, 37, 361, 4301, 60001, 954325, 16984577, 333572041]
InvBinConv [1, -1, -3, -1, 73, 699, 3001, -24697, -783999, -10946233]
TransSqrs [0, 0, 2, 30, 372, 4580, 58830, 801402, 11635400, 180129672]
TransNat0 [0, 0, 2, 18, 156, 1460, 15030, 170142, 2107448, 28393416]
TransNat1 [1, 1, 5, 31, 229, 1961, 19081, 207775, 2501801, 32989969]
PosHalf [1, 2, 8, 44, 304, 2512, 24064, 261536, 3173888, 42483968]
NegHalf [1, -2, 0, 4, 16, 48, 64, -800, -12288, -127232]

Lah:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
DiagRow2 [1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600, 199584000]
DiagRow3 [1, 12, 120, 1200, 12600, 141120, 1693440, 21772800, 299376000, 4390848000]
DiagRow4 [1, 20, 300, 4200, 58800, 846720, 12700800, 199584000, 3293136000, 57081024000]
DiagRow5 [1, 30, 630, 11760, 211680, 3810240, 69854400, 1317254400, 25686460800, 519437318400]
DiagRow6 [1, 42, 1176, 28224, 635040, 13970880, 307359360, 6849722880, 155831195520, 3636061228800]
DiagRow7 [1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480, 779155977600, 20777492736000]
DiagRow8 [1, 72, 3240, 118800, 3920400, 122316480, 3710266560, 111307996800, 3339239904000, 100919250432000]
DiagRow9 [1, 90, 4950, 217800, 8494200, 309188880, 10821610800, 371026656000, 12614906304000, 428906814336000]

Lah:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, 2, 6, 12, 20, 30, 42, 56, 72, 90]
DiagCol2 [0, 6, 36, 120, 300, 630, 1176, 2016, 3240, 4950]
DiagCol3 [0, 24, 240, 1200, 4200, 11760, 28224, 60480, 118800, 217800]
DiagCol4 [0, 120, 1800, 12600, 58800, 211680, 635040, 1663200, 3920400, 8494200]
DiagCol5 [0, 720, 15120, 141120, 846720, 3810240, 13970880, 43908480, 122316480, 309188880]
DiagCol6 [0, 5040, 141120, 1693440, 12700800, 69854400, 307359360, 1141620480, 3710266560, 10821610800]
DiagCol7 [0, 40320, 1451520, 21772800, 199584000, 1317254400, 6849722880, 29682132480, 111307996800, 371026656000]
DiagCol8 [0, 362880, 16329600, 299376000, 3293136000, 25686460800, 155831195520, 779155977600, 3339239904000, 12614906304000]
DiagCol9 [0, 3628800, 199584000, 4390848000, 57081024000, 519437318400, 3636061228800, 20777492736000, 100919250432000, 428906814336000]

Lah:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2 [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]
PolyRow3 [1, 13, 37, 73, 121, 181, 253, 337, 433, 541]
PolyRow4 [1, 73, 361, 1009, 2161, 3961, 6553, 10081, 14689, 20521]
PolyRow5 [1, 501, 4361, 17341, 48081, 108101, 211801, 376461, 622241, 972181]
PolyRow6 [1, 4051, 62701, 355951, 1279801, 3532651, 8201701, 16849351, 31599601, 55224451]
PolyRow7 [1, 37633, 1044205, 8488117, 39631369, 134415961, 369979093, 878797165, 1870458577, 3657065329]
PolyRow8 [1, 394353, 19748177, 230439553, 1398961761, 5834249681, 19047250993, 52324954977, 126422091713, 276573714481]
PolyRow9 [1, 4596553, 417787921, 7013527129, 55422807841, 284391878761, 1101705494833, 3501300491641, 9604726291009, 23514740267401]

Lah:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
PolyCol2 [1, 1, 5, 37, 361, 4361, 62701, 1044205, 19748177, 417787921]
PolyCol3 [1, 1, 7, 73, 1009, 17341, 355951, 8488117, 230439553, 7013527129]
PolyCol4 [1, 1, 9, 121, 2161, 48081, 1279801, 39631369, 1398961761, 55422807841]
PolyCol5 [1, 1, 11, 181, 3961, 108101, 3532651, 134415961, 5834249681, 284391878761]
PolyCol6 [1, 1, 13, 253, 6553, 211801, 8201701, 369979093, 19047250993, 1101705494833]
PolyCol7 [1, 1, 15, 337, 10081, 376461, 16849351, 878797165, 52324954977, 3501300491641]
PolyCol8 [1, 1, 17, 433, 14689, 622241, 31599601, 1870458577, 126422091713, 9604726291009]
PolyCol9 [1, 1, 19, 541, 20521, 972181, 55224451, 3657065329, 276573714481, 23514740267401]

Lah:Inv:Rev

[]

Lah:Inv:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, -2, 0]
Row3 [1, -6, 6, 0]
Row4 [1, -12, 36, -24, 0]
Row5 [1, -20, 120, -240, 120, 0]
Row6 [1, -30, 300, -1200, 1800, -720, 0]
Row7 [1, -42, 630, -4200, 12600, -15120, 5040, 0]
Row8 [1, -56, 1176, -11760, 58800, -141120, 141120, -40320, 0]
Row9 [1, -72, 2016, -28224, 211680, -846720, 1693440, -1451520, 362880, 0]

Lah:Inv:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, -2, 0], [1, -6, 6, 0], [1, -12, 36, -24, 0], [1, -20, 120, -240, 120, 0], [1, -30, 300, -1200, 1800, -720, 0], [1, -42, 630, -4200, 12600, -15120, 5040, 0], [1, -56, 1176, -11760, 58800, -141120, 141120, -40320, 0], [1, -72, 2016, -28224, 211680, -846720, 1693440, -1451520, 362880, 0]]
RevTabl [[1], [0, 1], [0, -2, 1], [0, 6, -6, 1], [0, -24, 36, -12, 1], [0, 120, -240, 120, -20, 1], [0, -720, 1800, -1200, 300, -30, 1], [0, 5040, -15120, 12600, -4200, 630, -42, 1], [0, -40320, 141120, -141120, 58800, -11760, 1176, -56, 1], [0, 362880, -1451520, 1693440, -846720, 211680, -28224, 2016, -72, 1]]
AntiDiag [[1], [1], [1, 0], [1, -2], [1, -6, 0], [1, -12, 6], [1, -20, 36, 0], [1, -30, 120, -24], [1, -42, 300, -240, 0], [1, -56, 630, -1200, 120]]
AccTabl [[1], [1, 1], [1, -1, -1], [1, -5, 1, 1], [1, -11, 25, 1, 1], [1, -19, 101, -139, -19, -19], [1, -29, 271, -929, 871, 151, 151], [1, -41, 589, -3611, 8989, -6131, -1091, -1091], [1, -55, 1121, -10639, 48161, -92959, 48161, 7841, 7841], [1, -71, 1945, -26279, 185401, -661319, 1032121, -419399, -56519, -56519]]
RevAccTabl [[1], [1, 1], [-1, -1, 1], [1, 1, -5, 1], [1, 1, 25, -11, 1], [-19, -19, -139, 101, -19, 1], [151, 151, 871, -929, 271, -29, 1], [-1091, -1091, -6131, 8989, -3611, 589, -41, 1], [7841, 7841, 48161, -92959, 48161, -10639, 1121, -55, 1], [-56519, -56519, -419399, 1032121, -661319, 185401, -26279, 1945, -71, 1]]
AccRevTabl [[1], [0, 1], [0, -2, -1], [0, 6, 0, 1], [0, -24, 12, 0, 1], [0, 120, -120, 0, -20, -19], [0, -720, 1080, -120, 180, 150, 151], [0, 5040, -10080, 2520, -1680, -1050, -1092, -1091], [0, -40320, 100800, -40320, 18480, 6720, 7896, 7840, 7841], [0, 362880, -1088640, 604800, -241920, -30240, -58464, -56448, -56520, -56519]]
DiffxTabl [[1], [1, 0], [1, -4, 0], [1, -12, 18, 0], [1, -24, 108, -96, 0], [1, -40, 360, -960, 600, 0], [1, -60, 900, -4800, 9000, -4320, 0], [1, -84, 1890, -16800, 63000, -90720, 35280, 0], [1, -112, 3528, -47040, 294000, -846720, 987840, -322560, 0], [1, -144, 6048, -112896, 1058400, -5080320, 11854080, -11612160, 3265920, 0]]

Lah:Inv:Rev Row sums

Trait Seq
RowSum [1, 1, -1, 1, 1, -19, 151, -1091, 7841, -56519]
EvenSum [1, 1, 1, 7, 37, 241, 2101, 18271, 201097, 2270017]
OddSum [0, 0, -2, -6, -36, -260, -1950, -19362, -193256, -2326536]
AltSum [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
AbsSum [1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553]
AccSum [1, 2, -1, -2, 17, -94, 487, -2386, 9473, -638]
AccRevSum [1, 1, -3, 7, -11, -39, 721, -7433, 68937, -621071]
DiagSum [1, 1, 1, -1, -5, -5, 17, 67, 19, -505]

Lah:Inv:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 6, 72, 240, 3600, 75600, 1411200, 10160640]
RowGcd [1, 1, 2, 6, 12, 20, 30, 42, 56, 72]
RowMax [1, 1, 2, 6, 36, 240, 1800, 15120, 141120, 1693440]
CentralE [1, -2, 36, -1200, 58800]
CentralO [1, -6, 120, -4200, 211680]
ColMiddle [1, 1, -2, -6, 36, 120, -1200, -4200, 58800, 211680]
ColLeft [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [1, 1, -3, 1, 73, -699, 3001, 24697, -783999, 10946233]
InvBinConv [1, -1, 5, -37, 361, -4301, 60001, -954325, 16984577, -333572041]
TransSqrs [0, 0, -2, 18, -84, 220, 1170, -30282, 416248, -4963464]
TransNat0 [0, 0, -2, 6, -12, -20, 570, -6342, 61096, -564552]
TransNat1 [1, 1, -3, 7, -11, -39, 721, -7433, 68937, -621071]
PosHalf [1, 2, 0, -4, 16, -48, 64, 800, -12288, 127232]
NegHalf [1, -2, 8, -44, 304, -2512, 24064, -261536, 3173888, -42483968]

Lah:Inv:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, -2, 6, -24, 120, -720, 5040, -40320, 362880, -3628800]
DiagRow2 [1, -6, 36, -240, 1800, -15120, 141120, -1451520, 16329600, -199584000]
DiagRow3 [1, -12, 120, -1200, 12600, -141120, 1693440, -21772800, 299376000, -4390848000]
DiagRow4 [1, -20, 300, -4200, 58800, -846720, 12700800, -199584000, 3293136000, -57081024000]
DiagRow5 [1, -30, 630, -11760, 211680, -3810240, 69854400, -1317254400, 25686460800, -519437318400]
DiagRow6 [1, -42, 1176, -28224, 635040, -13970880, 307359360, -6849722880, 155831195520, -3636061228800]
DiagRow7 [1, -56, 2016, -60480, 1663200, -43908480, 1141620480, -29682132480, 779155977600, -20777492736000]
DiagRow8 [1, -72, 3240, -118800, 3920400, -122316480, 3710266560, -111307996800, 3339239904000, -100919250432000]
DiagRow9 [1, -90, 4950, -217800, 8494200, -309188880, 10821610800, -371026656000, 12614906304000, -428906814336000]

Lah:Inv:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, -2, -6, -12, -20, -30, -42, -56, -72, -90]
DiagCol2 [0, 6, 36, 120, 300, 630, 1176, 2016, 3240, 4950]
DiagCol3 [0, -24, -240, -1200, -4200, -11760, -28224, -60480, -118800, -217800]
DiagCol4 [0, 120, 1800, 12600, 58800, 211680, 635040, 1663200, 3920400, 8494200]
DiagCol5 [0, -720, -15120, -141120, -846720, -3810240, -13970880, -43908480, -122316480, -309188880]
DiagCol6 [0, 5040, 141120, 1693440, 12700800, 69854400, 307359360, 1141620480, 3710266560, 10821610800]
DiagCol7 [0, -40320, -1451520, -21772800, -199584000, -1317254400, -6849722880, -29682132480, -111307996800, -371026656000]
DiagCol8 [0, 362880, 16329600, 299376000, 3293136000, 25686460800, 155831195520, 779155977600, 3339239904000, 12614906304000]
DiagCol9 [0, -3628800, -199584000, -4390848000, -57081024000, -519437318400, -3636061228800, -20777492736000, -100919250432000, -428906814336000]

Lah:Inv:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2 [1, -1, -3, -5, -7, -9, -11, -13, -15, -17]
PolyRow3 [1, 1, 13, 37, 73, 121, 181, 253, 337, 433]
PolyRow4 [1, 1, -71, -359, -1007, -2159, -3959, -6551, -10079, -14687]
PolyRow5 [1, -19, 441, 4261, 17201, 47901, 107881, 211541, 376161, 621901]
PolyRow6 [1, 151, -2699, -58949, -348599, -1267649, -3514499, -8176349, -16815599, -31556249]
PolyRow7 [1, -1091, 9157, 912745, 8127673, 38865541, 133017949, 367671697, 875252785, 1865299213]
PolyRow8 [1, 7841, 206193, -15139823, -212763487, -1350690879, -5726567279, -18837228367, -51952729023, -125808042527]
PolyRow9 [1, -56519, -8443151, 251548201, 6121704673, 52292822041, 275859706321, 1082041212169, 3461090604481, 9529552851193]

Lah:Inv:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, -1, 1, 1, -19, 151, -1091, 7841, -56519]
PolyCol2 [1, 1, -3, 13, -71, 441, -2699, 9157, 206193, -8443151]
PolyCol3 [1, 1, -5, 37, -359, 4261, -58949, 912745, -15139823, 251548201]
PolyCol4 [1, 1, -7, 73, -1007, 17201, -348599, 8127673, -212763487, 6121704673]
PolyCol5 [1, 1, -9, 121, -2159, 47901, -1267649, 38865541, -1350690879, 52292822041]
PolyCol6 [1, 1, -11, 181, -3959, 107881, -3514499, 133017949, -5726567279, 275859706321]
PolyCol7 [1, 1, -13, 253, -6551, 211541, -8176349, 367671697, -18837228367, 1082041212169]
PolyCol8 [1, 1, -15, 337, -10079, 376161, -16815599, 875252785, -51952729023, 3461090604481]
PolyCol9 [1, 1, -17, 433, -14687, 621901, -31556249, 1865299213, -125808042527, 9529552851193]