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Harmonic

['A358694', 'A109822']

Harmonic Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, 2, 1]
Row3 [0, 6, 4, 1]
Row4 [0, 24, 18, 7, 1]
Row5 [0, 120, 96, 46, 11, 1]
Row6 [0, 720, 600, 326, 101, 16, 1]
Row7 [0, 5040, 4320, 2556, 932, 197, 22, 1]
Row8 [0, 40320, 35280, 22212, 9080, 2311, 351, 29, 1]
Row9 [0, 362880, 322560, 212976, 94852, 27568, 5119, 583, 37, 1]

Harmonic Triangles

Flat Seq
Triangle [[1], [0, 1], [0, 2, 1], [0, 6, 4, 1], [0, 24, 18, 7, 1], [0, 120, 96, 46, 11, 1], [0, 720, 600, 326, 101, 16, 1], [0, 5040, 4320, 2556, 932, 197, 22, 1], [0, 40320, 35280, 22212, 9080, 2311, 351, 29, 1], [0, 362880, 322560, 212976, 94852, 27568, 5119, 583, 37, 1]]
RevTabl [[1], [1, 0], [1, 2, 0], [1, 4, 6, 0], [1, 7, 18, 24, 0], [1, 11, 46, 96, 120, 0], [1, 16, 101, 326, 600, 720, 0], [1, 22, 197, 932, 2556, 4320, 5040, 0], [1, 29, 351, 2311, 9080, 22212, 35280, 40320, 0], [1, 37, 583, 5119, 27568, 94852, 212976, 322560, 362880, 0]]
AntiDiag [[1], [0], [0, 1], [0, 2], [0, 6, 1], [0, 24, 4], [0, 120, 18, 1], [0, 720, 96, 7], [0, 5040, 600, 46, 1], [0, 40320, 4320, 326, 11]]
AccTabl [[1], [0, 1], [0, 2, 3], [0, 6, 10, 11], [0, 24, 42, 49, 50], [0, 120, 216, 262, 273, 274], [0, 720, 1320, 1646, 1747, 1763, 1764], [0, 5040, 9360, 11916, 12848, 13045, 13067, 13068], [0, 40320, 75600, 97812, 106892, 109203, 109554, 109583, 109584], [0, 362880, 685440, 898416, 993268, 1020836, 1025955, 1026538, 1026575, 1026576]]
RevAccTabl [[1], [1, 0], [3, 2, 0], [11, 10, 6, 0], [50, 49, 42, 24, 0], [274, 273, 262, 216, 120, 0], [1764, 1763, 1747, 1646, 1320, 720, 0], [13068, 13067, 13045, 12848, 11916, 9360, 5040, 0], [109584, 109583, 109554, 109203, 106892, 97812, 75600, 40320, 0], [1026576, 1026575, 1026538, 1025955, 1020836, 993268, 898416, 685440, 362880, 0]]
AccRevTabl [[1], [1, 1], [1, 3, 3], [1, 5, 11, 11], [1, 8, 26, 50, 50], [1, 12, 58, 154, 274, 274], [1, 17, 118, 444, 1044, 1764, 1764], [1, 23, 220, 1152, 3708, 8028, 13068, 13068], [1, 30, 381, 2692, 11772, 33984, 69264, 109584, 109584], [1, 38, 621, 5740, 33308, 128160, 341136, 663696, 1026576, 1026576]]
DiffxTabl [[1], [0, 2], [0, 4, 3], [0, 12, 12, 4], [0, 48, 54, 28, 5], [0, 240, 288, 184, 55, 6], [0, 1440, 1800, 1304, 505, 96, 7], [0, 10080, 12960, 10224, 4660, 1182, 154, 8], [0, 80640, 105840, 88848, 45400, 13866, 2457, 232, 9], [0, 725760, 967680, 851904, 474260, 165408, 35833, 4664, 333, 10]]

Harmonic Row sums

Trait Seq
RowSum [1, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576]
EvenSum [1, 0, 1, 4, 19, 107, 702, 5274, 44712, 422568]
OddSum [0, 1, 2, 7, 31, 167, 1062, 7794, 64872, 604008]
AltSum [1, -1, -1, -3, -12, -60, -360, -2520, -20160, -181440]
AbsSum [1, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576]
AccSum [1, 1, 5, 27, 165, 1145, 8960, 78344, 758548, 8066484]
AccRevSum [1, 2, 7, 28, 135, 773, 5152, 39268, 337292, 3225852]
DiagSum [1, 0, 1, 2, 7, 28, 139, 823, 5687, 44977]

Harmonic Transforms

Trans Seq
RowLcm [1, 1, 2, 12, 504, 121440, 59266800, 1084064113440, 103321840810930560, 6456945582111373908894720]
RowGcd [1, 1, 2, 2, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
CentralE [1, 2, 18, 326, 9080]
CentralO [0, 6, 96, 2556, 94852]
ColMiddle [1, 0, 2, 6, 18, 96, 326, 2556, 9080, 94852]
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, 31, 233, 2076, 21452, 252372, 3329349, 48644302]
InvBinConv [1, 1, -3, 7, -15, 46, -420, 5384, -62811, 656620]
TransSqrs [0, 1, 6, 31, 175, 1119, 8106, 66002, 598524, 5992036]
TransNat0 [0, 1, 4, 17, 85, 499, 3388, 26200, 227708, 2199276]
TransNat1 [1, 2, 7, 28, 135, 773, 5152, 39268, 337292, 3225852]
PosHalf [1, 1, 5, 33, 279, 2895, 35685, 509985, 8294895, 151335135]
NegHalf [1, 1, -3, 17, -133, 1315, -15675, 218505, -3485685, 62607195]

Harmonic Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, 2, 4, 7, 11, 16, 22, 29, 37, 46]
DiagRow2 [0, 6, 18, 46, 101, 197, 351, 583, 916, 1376]
DiagRow3 [0, 24, 96, 326, 932, 2311, 5119, 10366, 19526, 34662]
DiagRow4 [0, 120, 600, 2556, 9080, 27568, 73639, 177299, 392085, 808029]
DiagRow5 [0, 720, 4320, 22212, 94852, 342964, 1079354, 3029643, 7734663, 18239040]
DiagRow6 [0, 5040, 35280, 212976, 1066644, 4496284, 16369178, 52724894, 153275513, 408622073]
DiagRow7 [0, 40320, 322560, 2239344, 12905784, 62364908, 258795044, 944218666, 3090075848, 9219406943]
DiagRow8 [0, 362880, 3265920, 25659360, 167622984, 916001880, 4280337452, 17499398776, 63850536496, 211361047584]
DiagRow9 [0, 3628800, 36288000, 318540960, 2330016768, 14238041208, 74162765536, 336653747176, 1358262331112, 4951400140040]

Harmonic 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, 4, 18, 96, 600, 4320, 35280, 322560, 3265920, 36288000]
DiagCol3 [1, 7, 46, 326, 2556, 22212, 212976, 2239344, 25659360, 318540960]
DiagCol4 [1, 11, 101, 932, 9080, 94852, 1066644, 12905784, 167622984, 2330016768]
DiagCol5 [1, 16, 197, 2311, 27568, 342964, 4496284, 62364908, 916001880, 14238041208]
DiagCol6 [1, 22, 351, 5119, 73639, 1079354, 16369178, 258795044, 4280337452, 74162765536]
DiagCol7 [1, 29, 583, 10366, 177299, 3029643, 52724894, 944218666, 17499398776, 336653747176]
DiagCol8 [1, 37, 916, 19526, 392085, 7734663, 153275513, 3090075848, 63850536496, 1358262331112]
DiagCol9 [1, 46, 1376, 34662, 808029, 18239040, 408622073, 9219406943, 211361047584, 4951400140040]

Harmonic 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, 11, 36, 81, 152, 255, 396, 581, 816, 1107]
PolyRow4 [0, 50, 192, 504, 1088, 2070, 3600, 5852, 9024, 13338]
PolyRow5 [0, 274, 1200, 3600, 8800, 18750, 36144, 64540, 108480, 173610]
PolyRow6 [0, 1764, 8640, 29160, 79680, 188100, 398304, 775320, 1411200, 2431620]
PolyRow7 [0, 13068, 70560, 264600, 799680, 2072700, 4783968, 10084200, 19762560, 36480780]
PolyRow8 [0, 109584, 645120, 2661120, 8816640, 24897600, 62221824, 141214080, 296478720, 583737840]
PolyRow9 [0, 1026576, 6531840, 29393280, 105960960, 323870400, 871347456, 2118493440, 4743982080, 9923906160]

Harmonic Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576]
PolyCol2 [1, 2, 8, 36, 192, 1200, 8640, 70560, 645120, 6531840]
PolyCol3 [1, 3, 15, 81, 504, 3600, 29160, 264600, 2661120, 29393280]
PolyCol4 [1, 4, 24, 152, 1088, 8800, 79680, 799680, 8816640, 105960960]
PolyCol5 [1, 5, 35, 255, 2070, 18750, 188100, 2072700, 24897600, 323870400]
PolyCol6 [1, 6, 48, 396, 3600, 36144, 398304, 4783968, 62221824, 871347456]
PolyCol7 [1, 7, 63, 581, 5852, 64540, 775320, 10084200, 141214080, 2118493440]
PolyCol8 [1, 8, 80, 816, 9024, 108480, 1411200, 19762560, 296478720, 4743982080]
PolyCol9 [1, 9, 99, 1107, 13338, 173610, 2431620, 36480780, 583737840, 9923906160]

Harmonic:Inv

[]

Harmonic:Inv Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, -2, 1]
Row3 [0, 2, -4, 1]
Row4 [0, -2, 10, -7, 1]
Row5 [0, 2, -22, 31, -11, 1]
Row6 [0, -2, 46, -115, 75, -16, 1]
Row7 [0, 2, -94, 391, -415, 155, -22, 1]
Row8 [0, -2, 190, -1267, 2051, -1190, 287, -29, 1]
Row9 [0, 2, -382, 3991, -9471, 8001, -2912, 490, -37, 1]

Harmonic:Inv Triangles

Flat Seq
Triangle [[1], [0, 1], [0, -2, 1], [0, 2, -4, 1], [0, -2, 10, -7, 1], [0, 2, -22, 31, -11, 1], [0, -2, 46, -115, 75, -16, 1], [0, 2, -94, 391, -415, 155, -22, 1], [0, -2, 190, -1267, 2051, -1190, 287, -29, 1], [0, 2, -382, 3991, -9471, 8001, -2912, 490, -37, 1]]
RevTabl [[1], [1, 0], [1, -2, 0], [1, -4, 2, 0], [1, -7, 10, -2, 0], [1, -11, 31, -22, 2, 0], [1, -16, 75, -115, 46, -2, 0], [1, -22, 155, -415, 391, -94, 2, 0], [1, -29, 287, -1190, 2051, -1267, 190, -2, 0], [1, -37, 490, -2912, 8001, -9471, 3991, -382, 2, 0]]
AntiDiag [[1], [0], [0, 1], [0, -2], [0, 2, 1], [0, -2, -4], [0, 2, 10, 1], [0, -2, -22, -7], [0, 2, 46, 31, 1], [0, -2, -94, -115, -11]]
AccTabl [[1], [0, 1], [0, -2, -1], [0, 2, -2, -1], [0, -2, 8, 1, 2], [0, 2, -20, 11, 0, 1], [0, -2, 44, -71, 4, -12, -11], [0, 2, -92, 299, -116, 39, 17, 18], [0, -2, 188, -1079, 972, -218, 69, 40, 41], [0, 2, -380, 3611, -5860, 2141, -771, -281, -318, -317]]
RevAccTabl [[1], [1, 0], [-1, -2, 0], [-1, -2, 2, 0], [2, 1, 8, -2, 0], [1, 0, 11, -20, 2, 0], [-11, -12, 4, -71, 44, -2, 0], [18, 17, 39, -116, 299, -92, 2, 0], [41, 40, 69, -218, 972, -1079, 188, -2, 0], [-317, -318, -281, -771, 2141, -5860, 3611, -380, 2, 0]]
AccRevTabl [[1], [1, 1], [1, -1, -1], [1, -3, -1, -1], [1, -6, 4, 2, 2], [1, -10, 21, -1, 1, 1], [1, -15, 60, -55, -9, -11, -11], [1, -21, 134, -281, 110, 16, 18, 18], [1, -28, 259, -931, 1120, -147, 43, 41, 41], [1, -36, 454, -2458, 5543, -3928, 63, -319, -317, -317]]
DiffxTabl [[1], [0, 2], [0, -4, 3], [0, 4, -12, 4], [0, -4, 30, -28, 5], [0, 4, -66, 124, -55, 6], [0, -4, 138, -460, 375, -96, 7], [0, 4, -282, 1564, -2075, 930, -154, 8], [0, -4, 570, -5068, 10255, -7140, 2009, -232, 9], [0, 4, -1146, 15964, -47355, 48006, -20384, 3920, -333, 10]]

Harmonic:Inv Row sums

Trait Seq
RowSum [1, 1, -1, -1, 2, 1, -11, 18, 41, -317]
EvenSum [1, 0, 1, -4, 11, -33, 122, -531, 2529, -12802]
OddSum [0, 1, -2, 3, -9, 34, -133, 549, -2488, 12485]
AltSum [1, -1, 3, -7, 20, -67, 255, -1080, 5017, -25287]
AbsSum [1, 1, 3, 7, 20, 67, 255, 1080, 5017, 25287]
AccSum [1, 1, -3, -1, 9, -6, -48, 167, 11, -2173]
AccRevSum [1, 2, -1, -4, 3, 13, -40, -5, 399, -1314]
DiagSum [1, 0, 1, -2, 3, -6, 13, -31, 80, -222]

Harmonic:Inv Transforms

Trans Seq
RowLcm [1, 1, 2, 4, 70, 682, 27600, 5201242310, 1425701518570, 113987086706132640]
RowGcd [1, 1, 2, 2, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 2, 4, 10, 31, 115, 415, 2051, 9471]
CentralE [1, -2, 10, -115, 2051]
CentralO [0, 2, -22, 391, -9471]
ColMiddle [1, 0, -2, 2, 10, -22, -115, 391, 2051, -9471]
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, -5, 25, 46, -592, 302, 19087, -91010]
InvBinConv [1, 1, 5, 19, 97, 596, 4224, 33608, 294767, 2813068]
TransSqrs [0, 1, 2, -5, -9, 42, -17, -363, 1396, -227]
TransNat0 [0, 1, 0, -3, 1, 12, -29, -23, 358, -997]
TransNat1 [1, 2, -1, -4, 3, 13, -40, -5, 399, -1314]
PosHalf [1, 1, -3, 1, 11, -41, 21, 633, -4253, 10575]
NegHalf [1, 1, 5, 17, 71, 355, 2053, 13377, 96503, 761251]

Harmonic:Inv Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, -2, -4, -7, -11, -16, -22, -29, -37, -46]
DiagRow2 [0, 2, 10, 31, 75, 155, 287, 490, 786, 1200]
DiagRow3 [0, -2, -22, -115, -415, -1190, -2912, -6342, -12630, -23430]
DiagRow4 [0, 2, 46, 391, 2051, 8001, 25473, 69867, 170907, 381777]
DiagRow5 [0, -2, -94, -1267, -9471, -49476, -202314, -691383, -2058639, -5494632]
DiagRow6 [0, 2, 190, 3991, 41875, 289255, 1503139, 6342820, 22811932, 72263620]
DiagRow7 [0, -2, -382, -12355, -179855, -1626130, -10644964, -55044704, -237540160, -887912740]
DiagRow8 [0, 2, 766, 37831, 757251, 8887901, 72757685, 458070613, 2358391893, 10349606553]
DiagRow9 [0, -2, -1534, -115027, -3144031, -47583536, -484129646, -3690623937, -22557759081, -115704218058]

Harmonic:Inv Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, -2, 2, -2, 2, -2, 2, -2, 2, -2]
DiagCol2 [1, -4, 10, -22, 46, -94, 190, -382, 766, -1534]
DiagCol3 [1, -7, 31, -115, 391, -1267, 3991, -12355, 37831, -115027]
DiagCol4 [1, -11, 75, -415, 2051, -9471, 41875, -179855, 757251, -3144031]
DiagCol5 [1, -16, 155, -1190, 8001, -49476, 289255, -1626130, 8887901, -47583536]
DiagCol6 [1, -22, 287, -2912, 25473, -202314, 1503139, -10644964, 72757685, -484129646]
DiagCol7 [1, -29, 490, -6342, 69867, -691383, 6342820, -55044704, 458070613, -3690623937]
DiagCol8 [1, -37, 786, -12630, 170907, -2058639, 22811932, -237540160, 2358391893, -22557759081]
DiagCol9 [1, -46, 1200, -23430, 381777, -5494632, 72263620, -887912740, 10349606553, -115704218058]

Harmonic: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, -3, 8, 35, 84, 161, 272, 423]
PolyRow4 [0, 2, -4, -24, -40, -10, 132, 476, 1136, 2250]
PolyRow5 [0, 1, 20, -3, -152, -415, -564, -35, 2192, 7713]
PolyRow6 [0, -11, 12, 219, 280, -735, -3756, -8393, -10896, -1395]
PolyRow7 [0, 18, -204, -84, 2280, 5910, 2028, -26544, -96624, -201510]
PolyRow8 [0, 41, 268, -3183, -5608, 18865, 89556, 146153, -34448, -855783]
PolyRow9 [0, -317, 2292, 7125, -44312, -145665, 27948, 1081297, 3104400, 3980763]

Harmonic:Inv Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, -1, -1, 2, 1, -11, 18, 41, -317]
PolyCol2 [1, 2, 0, -4, -4, 20, 12, -204, 268, 2292]
PolyCol3 [1, 3, 3, -3, -24, -3, 219, -84, -3183, 7125]
PolyCol4 [1, 4, 8, 8, -40, -152, 280, 2280, -5608, -44312]
PolyCol5 [1, 5, 15, 35, -10, -415, -735, 5910, 18865, -145665]
PolyCol6 [1, 6, 24, 84, 132, -564, -3756, 2028, 89556, 27948]
PolyCol7 [1, 7, 35, 161, 476, -35, -8393, -26544, 146153, 1081297]
PolyCol8 [1, 8, 48, 272, 1136, 2192, -10896, -96624, -34448, 3104400]
PolyCol9 [1, 9, 63, 423, 2250, 7713, -1395, -201510, -855783, 3980763]

Harmonic:Rev

[]

Harmonic:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, 2, 0]
Row3 [1, 4, 6, 0]
Row4 [1, 7, 18, 24, 0]
Row5 [1, 11, 46, 96, 120, 0]
Row6 [1, 16, 101, 326, 600, 720, 0]
Row7 [1, 22, 197, 932, 2556, 4320, 5040, 0]
Row8 [1, 29, 351, 2311, 9080, 22212, 35280, 40320, 0]
Row9 [1, 37, 583, 5119, 27568, 94852, 212976, 322560, 362880, 0]

Harmonic:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, 2, 0], [1, 4, 6, 0], [1, 7, 18, 24, 0], [1, 11, 46, 96, 120, 0], [1, 16, 101, 326, 600, 720, 0], [1, 22, 197, 932, 2556, 4320, 5040, 0], [1, 29, 351, 2311, 9080, 22212, 35280, 40320, 0], [1, 37, 583, 5119, 27568, 94852, 212976, 322560, 362880, 0]]
RevTabl [[1], [0, 1], [0, 2, 1], [0, 6, 4, 1], [0, 24, 18, 7, 1], [0, 120, 96, 46, 11, 1], [0, 720, 600, 326, 101, 16, 1], [0, 5040, 4320, 2556, 932, 197, 22, 1], [0, 40320, 35280, 22212, 9080, 2311, 351, 29, 1], [0, 362880, 322560, 212976, 94852, 27568, 5119, 583, 37, 1]]
AntiDiag [[1], [1], [1, 0], [1, 2], [1, 4, 0], [1, 7, 6], [1, 11, 18, 0], [1, 16, 46, 24], [1, 22, 101, 96, 0], [1, 29, 197, 326, 120]]
AccTabl [[1], [1, 1], [1, 3, 3], [1, 5, 11, 11], [1, 8, 26, 50, 50], [1, 12, 58, 154, 274, 274], [1, 17, 118, 444, 1044, 1764, 1764], [1, 23, 220, 1152, 3708, 8028, 13068, 13068], [1, 30, 381, 2692, 11772, 33984, 69264, 109584, 109584], [1, 38, 621, 5740, 33308, 128160, 341136, 663696, 1026576, 1026576]]
RevAccTabl [[1], [1, 1], [3, 3, 1], [11, 11, 5, 1], [50, 50, 26, 8, 1], [274, 274, 154, 58, 12, 1], [1764, 1764, 1044, 444, 118, 17, 1], [13068, 13068, 8028, 3708, 1152, 220, 23, 1], [109584, 109584, 69264, 33984, 11772, 2692, 381, 30, 1], [1026576, 1026576, 663696, 341136, 128160, 33308, 5740, 621, 38, 1]]
AccRevTabl [[1], [0, 1], [0, 2, 3], [0, 6, 10, 11], [0, 24, 42, 49, 50], [0, 120, 216, 262, 273, 274], [0, 720, 1320, 1646, 1747, 1763, 1764], [0, 5040, 9360, 11916, 12848, 13045, 13067, 13068], [0, 40320, 75600, 97812, 106892, 109203, 109554, 109583, 109584], [0, 362880, 685440, 898416, 993268, 1020836, 1025955, 1026538, 1026575, 1026576]]
DiffxTabl [[1], [1, 0], [1, 4, 0], [1, 8, 18, 0], [1, 14, 54, 96, 0], [1, 22, 138, 384, 600, 0], [1, 32, 303, 1304, 3000, 4320, 0], [1, 44, 591, 3728, 12780, 25920, 35280, 0], [1, 58, 1053, 9244, 45400, 133272, 246960, 322560, 0], [1, 74, 1749, 20476, 137840, 569112, 1490832, 2580480, 3265920, 0]]

Harmonic:Rev Row sums

Trait Seq
RowSum [1, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576]
EvenSum [1, 1, 1, 7, 19, 167, 702, 7794, 44712, 604008]
OddSum [0, 0, 2, 4, 31, 107, 1062, 5274, 64872, 422568]
AltSum [1, 1, -1, 3, -12, 60, -360, 2520, -20160, 181440]
AbsSum [1, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576]
AccSum [1, 2, 7, 28, 135, 773, 5152, 39268, 337292, 3225852]
AccRevSum [1, 1, 5, 27, 165, 1145, 8960, 78344, 758548, 8066484]
DiagSum [1, 1, 1, 3, 5, 14, 30, 87, 220, 673]

Harmonic:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 12, 504, 121440, 59266800, 1084064113440, 103321840810930560, 6456945582111373908894720]
RowGcd [1, 1, 2, 2, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
CentralE [1, 2, 18, 326, 9080]
CentralO [1, 4, 46, 932, 27568]
ColMiddle [1, 1, 2, 4, 18, 46, 326, 932, 9080, 27568]
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, 31, 233, 2076, 21452, 252372, 3329349, 48644302]
InvBinConv [1, -1, -3, -7, -15, -46, -420, -5384, -62811, -656620]
TransSqrs [0, 0, 2, 28, 295, 2979, 30954, 339534, 3968572, 49557724]
TransNat0 [0, 0, 2, 16, 115, 871, 7196, 65276, 648964, 7039908]
TransNat1 [1, 1, 5, 27, 165, 1145, 8960, 78344, 758548, 8066484]
PosHalf [1, 2, 8, 36, 192, 1200, 8640, 70560, 645120, 6531840]
NegHalf [1, -2, 0, -4, -16, -80, -480, -3360, -26880, -241920]

Harmonic: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, 4, 18, 96, 600, 4320, 35280, 322560, 3265920, 36288000]
DiagRow3 [1, 7, 46, 326, 2556, 22212, 212976, 2239344, 25659360, 318540960]
DiagRow4 [1, 11, 101, 932, 9080, 94852, 1066644, 12905784, 167622984, 2330016768]
DiagRow5 [1, 16, 197, 2311, 27568, 342964, 4496284, 62364908, 916001880, 14238041208]
DiagRow6 [1, 22, 351, 5119, 73639, 1079354, 16369178, 258795044, 4280337452, 74162765536]
DiagRow7 [1, 29, 583, 10366, 177299, 3029643, 52724894, 944218666, 17499398776, 336653747176]
DiagRow8 [1, 37, 916, 19526, 392085, 7734663, 153275513, 3090075848, 63850536496, 1358262331112]
DiagRow9 [1, 46, 1376, 34662, 808029, 18239040, 408622073, 9219406943, 211361047584, 4951400140040]

Harmonic:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, 2, 4, 7, 11, 16, 22, 29, 37, 46]
DiagCol2 [0, 6, 18, 46, 101, 197, 351, 583, 916, 1376]
DiagCol3 [0, 24, 96, 326, 932, 2311, 5119, 10366, 19526, 34662]
DiagCol4 [0, 120, 600, 2556, 9080, 27568, 73639, 177299, 392085, 808029]
DiagCol5 [0, 720, 4320, 22212, 94852, 342964, 1079354, 3029643, 7734663, 18239040]
DiagCol6 [0, 5040, 35280, 212976, 1066644, 4496284, 16369178, 52724894, 153275513, 408622073]
DiagCol7 [0, 40320, 322560, 2239344, 12905784, 62364908, 258795044, 944218666, 3090075848, 9219406943]
DiagCol8 [0, 362880, 3265920, 25659360, 167622984, 916001880, 4280337452, 17499398776, 63850536496, 211361047584]
DiagCol9 [0, 3628800, 36288000, 318540960, 2330016768, 14238041208, 74162765536, 336653747176, 1358262331112, 4951400140040]

Harmonic: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, 11, 33, 67, 113, 171, 241, 323, 417, 523]
PolyRow4 [1, 50, 279, 832, 1853, 3486, 5875, 9164, 13497, 19018]
PolyRow5 [1, 274, 2895, 12760, 37645, 88206, 177979, 323380, 543705, 861130]
PolyRow6 [1, 1764, 35685, 233320, 913425, 2668356, 6450469, 13658520, 26224065, 46697860]
PolyRow7 [1, 13068, 509985, 4957960, 25784745, 93969036, 272259673, 672023640, 1473722865, 2951019820]
PolyRow8 [1, 109584, 8294895, 120097600, 830332965, 3776635296, 13118043379, 37751838720, 94571849385, 212971432240]
PolyRow9 [1, 1026576, 151335135, 3266979520, 30043399365, 170592047136, 710506242691, 2384291583360, 6823627559145, 17282558344240]

Harmonic:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576]
PolyCol2 [1, 1, 5, 33, 279, 2895, 35685, 509985, 8294895, 151335135]
PolyCol3 [1, 1, 7, 67, 832, 12760, 233320, 4957960, 120097600, 3266979520]
PolyCol4 [1, 1, 9, 113, 1853, 37645, 913425, 25784745, 830332965, 30043399365]
PolyCol5 [1, 1, 11, 171, 3486, 88206, 2668356, 93969036, 3776635296, 170592047136]
PolyCol6 [1, 1, 13, 241, 5875, 177979, 6450469, 272259673, 13118043379, 710506242691]
PolyCol7 [1, 1, 15, 323, 9164, 323380, 13658520, 672023640, 37751838720, 2384291583360]
PolyCol8 [1, 1, 17, 417, 13497, 543705, 26224065, 1473722865, 94571849385, 6823627559145]
PolyCol9 [1, 1, 19, 523, 19018, 861130, 46697860, 2951019820, 212971432240, 17282558344240]

Harmonic:Inv:Rev

[]

Harmonic:Inv:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, -2, 0]
Row3 [1, -4, 2, 0]
Row4 [1, -7, 10, -2, 0]
Row5 [1, -11, 31, -22, 2, 0]
Row6 [1, -16, 75, -115, 46, -2, 0]
Row7 [1, -22, 155, -415, 391, -94, 2, 0]
Row8 [1, -29, 287, -1190, 2051, -1267, 190, -2, 0]
Row9 [1, -37, 490, -2912, 8001, -9471, 3991, -382, 2, 0]

Harmonic:Inv:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, -2, 0], [1, -4, 2, 0], [1, -7, 10, -2, 0], [1, -11, 31, -22, 2, 0], [1, -16, 75, -115, 46, -2, 0], [1, -22, 155, -415, 391, -94, 2, 0], [1, -29, 287, -1190, 2051, -1267, 190, -2, 0], [1, -37, 490, -2912, 8001, -9471, 3991, -382, 2, 0]]
RevTabl [[1], [0, 1], [0, -2, 1], [0, 2, -4, 1], [0, -2, 10, -7, 1], [0, 2, -22, 31, -11, 1], [0, -2, 46, -115, 75, -16, 1], [0, 2, -94, 391, -415, 155, -22, 1], [0, -2, 190, -1267, 2051, -1190, 287, -29, 1], [0, 2, -382, 3991, -9471, 8001, -2912, 490, -37, 1]]
AntiDiag [[1], [1], [1, 0], [1, -2], [1, -4, 0], [1, -7, 2], [1, -11, 10, 0], [1, -16, 31, -2], [1, -22, 75, -22, 0], [1, -29, 155, -115, 2]]
AccTabl [[1], [1, 1], [1, -1, -1], [1, -3, -1, -1], [1, -6, 4, 2, 2], [1, -10, 21, -1, 1, 1], [1, -15, 60, -55, -9, -11, -11], [1, -21, 134, -281, 110, 16, 18, 18], [1, -28, 259, -931, 1120, -147, 43, 41, 41], [1, -36, 454, -2458, 5543, -3928, 63, -319, -317, -317]]
RevAccTabl [[1], [1, 1], [-1, -1, 1], [-1, -1, -3, 1], [2, 2, 4, -6, 1], [1, 1, -1, 21, -10, 1], [-11, -11, -9, -55, 60, -15, 1], [18, 18, 16, 110, -281, 134, -21, 1], [41, 41, 43, -147, 1120, -931, 259, -28, 1], [-317, -317, -319, 63, -3928, 5543, -2458, 454, -36, 1]]
AccRevTabl [[1], [0, 1], [0, -2, -1], [0, 2, -2, -1], [0, -2, 8, 1, 2], [0, 2, -20, 11, 0, 1], [0, -2, 44, -71, 4, -12, -11], [0, 2, -92, 299, -116, 39, 17, 18], [0, -2, 188, -1079, 972, -218, 69, 40, 41], [0, 2, -380, 3611, -5860, 2141, -771, -281, -318, -317]]
DiffxTabl [[1], [1, 0], [1, -4, 0], [1, -8, 6, 0], [1, -14, 30, -8, 0], [1, -22, 93, -88, 10, 0], [1, -32, 225, -460, 230, -12, 0], [1, -44, 465, -1660, 1955, -564, 14, 0], [1, -58, 861, -4760, 10255, -7602, 1330, -16, 0], [1, -74, 1470, -11648, 40005, -56826, 27937, -3056, 18, 0]]

Harmonic:Inv:Rev Row sums

Trait Seq
RowSum [1, 1, -1, -1, 2, 1, -11, 18, 41, -317]
EvenSum [1, 1, 1, 3, 11, 34, 122, 549, 2529, 12485]
OddSum [0, 0, -2, -4, -9, -33, -133, -531, -2488, -12802]
AltSum [1, 1, 3, 7, 20, 67, 255, 1080, 5017, 25287]
AbsSum [1, 1, 3, 7, 20, 67, 255, 1080, 5017, 25287]
AccSum [1, 2, -1, -4, 3, 13, -40, -5, 399, -1314]
AccRevSum [1, 1, -3, -1, 9, -6, -48, 167, 11, -2173]
DiagSum [1, 1, 1, -1, -3, -4, 0, 14, 32, 14]

Harmonic:Inv:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 4, 70, 682, 27600, 5201242310, 1425701518570, 113987086706132640]
RowGcd [1, 1, 2, 2, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 2, 4, 10, 31, 115, 415, 2051, 9471]
CentralE [1, -2, 10, -115, 2051]
CentralO [1, -4, 31, -415, 8001]
ColMiddle [1, 1, -2, -4, 10, 31, -115, -415, 2051, 8001]
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, -5, 25, 46, -592, 302, 19087, -91010]
InvBinConv [1, -1, 5, -19, 97, -596, 4224, -33608, 294767, -2813068]
TransSqrs [0, 0, -2, 4, 15, -53, -65, 841, -1708, -7958]
TransNat0 [0, 0, -2, 0, 7, -7, -37, 149, -30, -1856]
TransNat1 [1, 1, -3, -1, 9, -6, -48, 167, 11, -2173]
PosHalf [1, 2, 0, -4, -4, 20, 12, -204, 268, 2292]
NegHalf [1, -2, 8, -28, 116, -548, 2884, -16644, 104132, -700100]

Harmonic:Inv:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, -2, 2, -2, 2, -2, 2, -2, 2, -2]
DiagRow2 [1, -4, 10, -22, 46, -94, 190, -382, 766, -1534]
DiagRow3 [1, -7, 31, -115, 391, -1267, 3991, -12355, 37831, -115027]
DiagRow4 [1, -11, 75, -415, 2051, -9471, 41875, -179855, 757251, -3144031]
DiagRow5 [1, -16, 155, -1190, 8001, -49476, 289255, -1626130, 8887901, -47583536]
DiagRow6 [1, -22, 287, -2912, 25473, -202314, 1503139, -10644964, 72757685, -484129646]
DiagRow7 [1, -29, 490, -6342, 69867, -691383, 6342820, -55044704, 458070613, -3690623937]
DiagRow8 [1, -37, 786, -12630, 170907, -2058639, 22811932, -237540160, 2358391893, -22557759081]
DiagRow9 [1, -46, 1200, -23430, 381777, -5494632, 72263620, -887912740, 10349606553, -115704218058]

Harmonic:Inv:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, -2, -4, -7, -11, -16, -22, -29, -37, -46]
DiagCol2 [0, 2, 10, 31, 75, 155, 287, 490, 786, 1200]
DiagCol3 [0, -2, -22, -115, -415, -1190, -2912, -6342, -12630, -23430]
DiagCol4 [0, 2, 46, 391, 2051, 8001, 25473, 69867, 170907, 381777]
DiagCol5 [0, -2, -94, -1267, -9471, -49476, -202314, -691383, -2058639, -5494632]
DiagCol6 [0, 2, 190, 3991, 41875, 289255, 1503139, 6342820, 22811932, 72263620]
DiagCol7 [0, -2, -382, -12355, -179855, -1626130, -10644964, -55044704, -237540160, -887912740]
DiagCol8 [0, 2, 766, 37831, 757251, 8887901, 72757685, 458070613, 2358391893, 10349606553]
DiagCol9 [0, -2, -1534, -115027, -3144031, -47583536, -484129646, -3690623937, -22557759081, -115704218058]

Harmonic: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, 1, 7, 17, 31, 49, 71, 97, 127]
PolyRow4 [1, 2, 11, 16, 5, -34, -113, -244, -439, -710]
PolyRow5 [1, 1, -41, -185, -443, -779, -1109, -1301, -1175, -503]
PolyRow6 [1, -11, 21, 763, 3505, 9921, 21829, 40951, 68673, 105805]
PolyRow7 [1, 18, 633, 412, -12135, -66234, -215087, -540672, -1157103, -2212550]
PolyRow8 [1, 41, -4253, -37247, -98563, -6719, 863791, 3941897, 11905753, 29204857]
PolyRow9 [1, -317, 10575, 359431, 2390797, 8348691, 18739003, 25529575, -374439, -128861693]

Harmonic:Inv:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, -1, -1, 2, 1, -11, 18, 41, -317]
PolyCol2 [1, 1, -3, 1, 11, -41, 21, 633, -4253, 10575]
PolyCol3 [1, 1, -5, 7, 16, -185, 763, 412, -37247, 359431]
PolyCol4 [1, 1, -7, 17, 5, -443, 3505, -12135, -98563, 2390797]
PolyCol5 [1, 1, -9, 31, -34, -779, 9921, -66234, -6719, 8348691]
PolyCol6 [1, 1, -11, 49, -113, -1109, 21829, -215087, 863791, 18739003]
PolyCol7 [1, 1, -13, 71, -244, -1301, 40951, -540672, 3941897, 25529575]
PolyCol8 [1, 1, -15, 97, -439, -1175, 68673, -1157103, 11905753, -374439]
PolyCol9 [1, 1, -17, 127, -710, -503, 105805, -2212550, 29204857, -128861693]