['A137452', 'A061356', 'A139526']
Abel Triangle view
| Row | Seq |
|---|---|
| Row0 | [1] |
| Row1 | [0, 1] |
| Row2 | [0, 2, 1] |
| Row3 | [0, 9, 6, 1] |
| Row4 | [0, 64, 48, 12, 1] |
| Row5 | [0, 625, 500, 150, 20, 1] |
| Row6 | [0, 7776, 6480, 2160, 360, 30, 1] |
| Row7 | [0, 117649, 100842, 36015, 6860, 735, 42, 1] |
| Row8 | [0, 2097152, 1835008, 688128, 143360, 17920, 1344, 56, 1] |
| Row9 | [0, 43046721, 38263752, 14880348, 3306744, 459270, 40824, 2268, 72, 1] |
Abel Triangles
| Flat | Seq |
|---|---|
| Triangle | [[1], [0, 1], [0, 2, 1], [0, 9, 6, 1], [0, 64, 48, 12, 1], [0, 625, 500, 150, 20, 1], [0, 7776, 6480, 2160, 360, 30, 1], [0, 117649, 100842, 36015, 6860, 735, 42, 1], [0, 2097152, 1835008, 688128, 143360, 17920, 1344, 56, 1], [0, 43046721, 38263752, 14880348, 3306744, 459270, 40824, 2268, 72, 1]] |
| RevTabl | [[1], [1, 0], [1, 2, 0], [1, 6, 9, 0], [1, 12, 48, 64, 0], [1, 20, 150, 500, 625, 0], [1, 30, 360, 2160, 6480, 7776, 0], [1, 42, 735, 6860, 36015, 100842, 117649, 0], [1, 56, 1344, 17920, 143360, 688128, 1835008, 2097152, 0], [1, 72, 2268, 40824, 459270, 3306744, 14880348, 38263752, 43046721, 0]] |
| AntiDiag | [[1], [0], [0, 1], [0, 2], [0, 9, 1], [0, 64, 6], [0, 625, 48, 1], [0, 7776, 500, 12], [0, 117649, 6480, 150, 1], [0, 2097152, 100842, 2160, 20]] |
| AccTabl | [[1], [0, 1], [0, 2, 3], [0, 9, 15, 16], [0, 64, 112, 124, 125], [0, 625, 1125, 1275, 1295, 1296], [0, 7776, 14256, 16416, 16776, 16806, 16807], [0, 117649, 218491, 254506, 261366, 262101, 262143, 262144], [0, 2097152, 3932160, 4620288, 4763648, 4781568, 4782912, 4782968, 4782969], [0, 43046721, 81310473, 96190821, 99497565, 99956835, 99997659, 99999927, 99999999, 100000000]] |
| RevAccTabl | [[1], [1, 0], [3, 2, 0], [16, 15, 9, 0], [125, 124, 112, 64, 0], [1296, 1295, 1275, 1125, 625, 0], [16807, 16806, 16776, 16416, 14256, 7776, 0], [262144, 262143, 262101, 261366, 254506, 218491, 117649, 0], [4782969, 4782968, 4782912, 4781568, 4763648, 4620288, 3932160, 2097152, 0], [100000000, 99999999, 99999927, 99997659, 99956835, 99497565, 96190821, 81310473, 43046721, 0]] |
| AccRevTabl | [[1], [1, 1], [1, 3, 3], [1, 7, 16, 16], [1, 13, 61, 125, 125], [1, 21, 171, 671, 1296, 1296], [1, 31, 391, 2551, 9031, 16807, 16807], [1, 43, 778, 7638, 43653, 144495, 262144, 262144], [1, 57, 1401, 19321, 162681, 850809, 2685817, 4782969, 4782969], [1, 73, 2341, 43165, 502435, 3809179, 18689527, 56953279, 100000000, 100000000]] |
| DiffxTabl | [[1], [0, 2], [0, 4, 3], [0, 18, 18, 4], [0, 128, 144, 48, 5], [0, 1250, 1500, 600, 100, 6], [0, 15552, 19440, 8640, 1800, 180, 7], [0, 235298, 302526, 144060, 34300, 4410, 294, 8], [0, 4194304, 5505024, 2752512, 716800, 107520, 9408, 448, 9], [0, 86093442, 114791256, 59521392, 16533720, 2755620, 285768, 18144, 648, 10]] |
Abel Row sums
| Trait | Seq |
|---|---|
| RowSum | [1, 1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000] |
| EvenSum | [1, 0, 1, 6, 49, 520, 6841, 107744, 1979713, 41611392] |
| OddSum | [0, 1, 2, 10, 76, 776, 9966, 154400, 2803256, 58388608] |
| AltSum | [1, -1, -1, -4, -27, -256, -3125, -46656, -823543, -16777216] |
| AbsSum | [1, 1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000] |
| AccSum | [1, 1, 5, 40, 425, 5616, 88837, 1638400, 34543665, 820000000] |
| AccRevSum | [1, 2, 7, 40, 325, 3456, 45619, 720896, 13286025, 280000000] |
| DiagSum | [1, 0, 1, 2, 10, 70, 674, 8288, 124280, 2200174] |
Abel Transforms
| Trans | Seq |
|---|---|
| RowLcm | [1, 1, 2, 18, 192, 7500, 38880, 7058940, 220200960, 12053081880] |
| RowGcd | [1, 1, 2, 3, 4, 5, 6, 7, 8, 9] |
| RowMax | [1, 1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721] |
| CentralE | [1, 2, 48, 2160, 143360] |
| CentralO | [0, 9, 500, 36015, 3306744] |
| ColMiddle | [1, 0, 2, 9, 48, 500, 2160, 36015, 143360, 3306744] |
| 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, 46, 593, 9726, 192637, 4457580, 117769409, 3492894070] |
| InvBinConv | [1, 1, -3, 10, -15, -474, 12565, -258572, 5136705, -102255290] |
| TransSqrs | [0, 1, 6, 42, 380, 4320, 59682, 974848, 18423288, 396000000] |
| TransNat0 | [0, 1, 4, 24, 200, 2160, 28812, 458752, 8503056, 180000000] |
| TransNat1 | [1, 2, 7, 40, 325, 3456, 45619, 720896, 13286025, 280000000] |
| PosHalf | [1, 1, 5, 49, 729, 14641, 371293, 11390625, 410338673, 16983563041] |
| NegHalf | [1, 1, -3, 25, -343, 6561, -161051, 4826809, -170859375, 6975757441] |
Abel 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, 9, 48, 150, 360, 735, 1344, 2268, 3600, 5445] |
| DiagRow3 | [0, 64, 500, 2160, 6860, 17920, 40824, 84000, 159720, 285120] |
| DiagRow4 | [0, 625, 6480, 36015, 143360, 459270, 1260000, 3074610, 6842880, 14137695] |
| DiagRow5 | [0, 7776, 100842, 688128, 3306744, 12600000, 40584852, 114960384, 294064056, 692179488] |
| DiagRow6 | [0, 117649, 1835008, 14880348, 84000000, 372027810, 1379524608, 4459971516, 12920683776, 34206046875] |
| DiagRow7 | [0, 2097152, 38263752, 360000000, 2338460520, 11824496640, 49696825464, 180889572864, 586389375000, 1727382159360] |
| DiagRow8 | [0, 43046721, 900000000, 9646149645, 70946979840, 403786706895, 1899340515072, 7696360546875, 27638114549760, 89777998265670] |
| DiagRow9 | [0, 1000000000, 23579476910, 283787919360, 2332989862060, 14772648450560, 76963605468750, 343940981063680, 1356645307125680, 4822114348846080] |
Abel Diagonals as columns
| DiagCol | Seq |
|---|---|
| DiagCol0 | [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
| DiagCol1 | [1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000] |
| DiagCol2 | [1, 6, 48, 500, 6480, 100842, 1835008, 38263752, 900000000, 23579476910] |
| DiagCol3 | [1, 12, 150, 2160, 36015, 688128, 14880348, 360000000, 9646149645, 283787919360] |
| DiagCol4 | [1, 20, 360, 6860, 143360, 3306744, 84000000, 2338460520, 70946979840, 2332989862060] |
| DiagCol5 | [1, 30, 735, 17920, 459270, 12600000, 372027810, 11824496640, 403786706895, 14772648450560] |
| DiagCol6 | [1, 42, 1344, 40824, 1260000, 40584852, 1379524608, 49696825464, 1899340515072, 76963605468750] |
| DiagCol7 | [1, 56, 2268, 84000, 3074610, 114960384, 4459971516, 180889572864, 7696360546875, 343940981063680] |
| DiagCol8 | [1, 72, 3600, 159720, 6842880, 294064056, 12920683776, 586389375000, 27638114549760, 1356645307125680] |
| DiagCol9 | [1, 90, 5445, 285120, 14137695, 692179488, 34206046875, 1727382159360, 89777998265670, 4822114348846080] |
Abel 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, 16, 50, 108, 196, 320, 486, 700, 968, 1296] |
| PolyRow4 | [0, 125, 432, 1029, 2048, 3645, 6000, 9317, 13824, 19773] |
| PolyRow5 | [0, 1296, 4802, 12288, 26244, 50000, 87846, 145152, 228488, 345744] |
| PolyRow6 | [0, 16807, 65536, 177147, 400000, 805255, 1492992, 2599051, 4302592, 6834375] |
| PolyRow7 | [0, 262144, 1062882, 3000000, 7086244, 14929920, 28960854, 52706752, 91125000, 150994944] |
| PolyRow8 | [0, 4782969, 20000000, 58461513, 143327232, 313742585, 632481024, 1196015625, 2147483648, 3693048057] |
| PolyRow9 | [0, 100000000, 428717762, 1289945088, 3262922884, 7378945280, 15377343750, 30064771072, 55806059528, 99179645184] |
Abel Polynomial values as columns
| PolyCol | Seq |
|---|---|
| PolyCol0 | [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
| PolyCol1 | [1, 1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000] |
| PolyCol2 | [1, 2, 8, 50, 432, 4802, 65536, 1062882, 20000000, 428717762] |
| PolyCol3 | [1, 3, 15, 108, 1029, 12288, 177147, 3000000, 58461513, 1289945088] |
| PolyCol4 | [1, 4, 24, 196, 2048, 26244, 400000, 7086244, 143327232, 3262922884] |
| PolyCol5 | [1, 5, 35, 320, 3645, 50000, 805255, 14929920, 313742585, 7378945280] |
| PolyCol6 | [1, 6, 48, 486, 6000, 87846, 1492992, 28960854, 632481024, 15377343750] |
| PolyCol7 | [1, 7, 63, 700, 9317, 145152, 2599051, 52706752, 1196015625, 30064771072] |
| PolyCol8 | [1, 8, 80, 968, 13824, 228488, 4302592, 91125000, 2147483648, 55806059528] |
| PolyCol9 | [1, 9, 99, 1296, 19773, 345744, 6834375, 150994944, 3693048057, 99179645184] |
[]
Abel:Inv Triangle view
| Row | Seq |
|---|---|
| Row0 | [1] |
| Row1 | [0, 1] |
| Row2 | [0, -2, 1] |
| Row3 | [0, 3, -6, 1] |
| Row4 | [0, -4, 24, -12, 1] |
| Row5 | [0, 5, -80, 90, -20, 1] |
| Row6 | [0, -6, 240, -540, 240, -30, 1] |
| Row7 | [0, 7, -672, 2835, -2240, 525, -42, 1] |
| Row8 | [0, -8, 1792, -13608, 17920, -7000, 1008, -56, 1] |
| Row9 | [0, 9, -4608, 61236, -129024, 78750, -18144, 1764, -72, 1] |
Abel:Inv Triangles
| Flat | Seq |
|---|---|
| Triangle | [[1], [0, 1], [0, -2, 1], [0, 3, -6, 1], [0, -4, 24, -12, 1], [0, 5, -80, 90, -20, 1], [0, -6, 240, -540, 240, -30, 1], [0, 7, -672, 2835, -2240, 525, -42, 1], [0, -8, 1792, -13608, 17920, -7000, 1008, -56, 1], [0, 9, -4608, 61236, -129024, 78750, -18144, 1764, -72, 1]] |
| RevTabl | [[1], [1, 0], [1, -2, 0], [1, -6, 3, 0], [1, -12, 24, -4, 0], [1, -20, 90, -80, 5, 0], [1, -30, 240, -540, 240, -6, 0], [1, -42, 525, -2240, 2835, -672, 7, 0], [1, -56, 1008, -7000, 17920, -13608, 1792, -8, 0], [1, -72, 1764, -18144, 78750, -129024, 61236, -4608, 9, 0]] |
| AntiDiag | [[1], [0], [0, 1], [0, -2], [0, 3, 1], [0, -4, -6], [0, 5, 24, 1], [0, -6, -80, -12], [0, 7, 240, 90, 1], [0, -8, -672, -540, -20]] |
| AccTabl | [[1], [0, 1], [0, -2, -1], [0, 3, -3, -2], [0, -4, 20, 8, 9], [0, 5, -75, 15, -5, -4], [0, -6, 234, -306, -66, -96, -95], [0, 7, -665, 2170, -70, 455, 413, 414], [0, -8, 1784, -11824, 6096, -904, 104, 48, 49], [0, 9, -4599, 56637, -72387, 6363, -11781, -10017, -10089, -10088]] |
| RevAccTabl | [[1], [1, 0], [-1, -2, 0], [-2, -3, 3, 0], [9, 8, 20, -4, 0], [-4, -5, 15, -75, 5, 0], [-95, -96, -66, -306, 234, -6, 0], [414, 413, 455, -70, 2170, -665, 7, 0], [49, 48, 104, -904, 6096, -11824, 1784, -8, 0], [-10088, -10089, -10017, -11781, 6363, -72387, 56637, -4599, 9, 0]] |
| AccRevTabl | [[1], [1, 1], [1, -1, -1], [1, -5, -2, -2], [1, -11, 13, 9, 9], [1, -19, 71, -9, -4, -4], [1, -29, 211, -329, -89, -95, -95], [1, -41, 484, -1756, 1079, 407, 414, 414], [1, -55, 953, -6047, 11873, -1735, 57, 49, 49], [1, -71, 1693, -16451, 62299, -66725, -5489, -10097, -10088, -10088]] |
| DiffxTabl | [[1], [0, 2], [0, -4, 3], [0, 6, -18, 4], [0, -8, 72, -48, 5], [0, 10, -240, 360, -100, 6], [0, -12, 720, -2160, 1200, -180, 7], [0, 14, -2016, 11340, -11200, 3150, -294, 8], [0, -16, 5376, -54432, 89600, -42000, 7056, -448, 9], [0, 18, -13824, 244944, -645120, 472500, -127008, 14112, -648, 10]] |
Abel:Inv Row sums
| Trait | Seq |
|---|---|
| RowSum | [1, 1, -1, -2, 9, -4, -95, 414, 49, -10088] |
| EvenSum | [1, 0, 1, -6, 25, -100, 481, -2954, 20721, -151848] |
| OddSum | [0, 1, -2, 4, -16, 96, -576, 3368, -20672, 141760] |
| AltSum | [1, -1, 3, -10, 41, -196, 1057, -6322, 41393, -293608] |
| AbsSum | [1, 1, 3, 10, 41, 196, 1057, 6322, 41393, 293608] |
| AccSum | [1, 1, -3, -2, 33, -64, -335, 2724, -4655, -55952] |
| AccRevSum | [1, 2, -1, -8, 21, 36, -425, 1002, 5145, -55016] |
| DiagSum | [1, 0, 1, -2, 4, -10, 30, -98, 338, -1240] |
Abel:Inv Transforms
| Trans | Seq |
|---|---|
| RowLcm | [1, 1, 2, 6, 24, 720, 2160, 907200, 108864000, 137168640000] |
| RowGcd | [1, 1, 2, 3, 4, 5, 6, 7, 8, 9] |
| RowMax | [1, 1, 2, 6, 24, 90, 540, 2835, 17920, 129024] |
| CentralE | [1, -2, 24, -540, 17920] |
| CentralO | [0, 3, -80, 2835, -129024] |
| ColMiddle | [1, 0, -2, 3, 24, -80, -540, 2835, 17920, -129024] |
| 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, -8, 81, 26, -3815, 17494, 178241, -2817746] |
| InvBinConv | [1, 1, 5, 28, 209, 1826, 18217, 203106, 2487361, 33077566] |
| TransSqrs | [0, 1, 2, -12, 0, 200, -780, -1344, 30016, -134208] |
| TransNat0 | [0, 1, 0, -6, 12, 40, -330, 588, 5096, -44928] |
| TransNat1 | [1, 2, -1, -8, 21, 36, -425, 1002, 5145, -55016] |
| PosHalf | [1, 1, -3, 1, 41, -239, 229, 8401, -87151, 324577] |
| NegHalf | [1, 1, 5, 25, 153, 1121, 9373, 87417, 898033, 10052353] |
Abel: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, 3, 24, 90, 240, 525, 1008, 1764, 2880, 4455] |
| DiagRow3 | [0, -4, -80, -540, -2240, -7000, -18144, -41160, -84480, -160380] |
| DiagRow4 | [0, 5, 240, 2835, 17920, 78750, 272160, 792330, 2027520, 4691115] |
| DiagRow5 | [0, -6, -672, -13608, -129024, -787500, -3592512, -13311144, -42172416, -118216098] |
| DiagRow6 | [0, 7, 1792, 61236, 860160, 7218750, 43110144, 201885684, 787218432, 2659862205] |
| DiagRow7 | [0, -8, -4608, -262440, -5406720, -61875000, -480370176, -2826399576, -13495173120, -54717165360] |
| DiagRow8 | [0, 9, 11520, 1082565, 32440320, 502734375, 5043886848, 37096494435, 215922769920, 1046465787510] |
| DiagRow9 | [0, -10, -28160, -4330260, -187432960, -3910156250, -50438868480, -461645264080, -3262832967680, -18836384175180] |
Abel:Inv Diagonals as columns
| DiagCol | Seq |
|---|---|
| DiagCol0 | [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
| DiagCol1 | [1, -2, 3, -4, 5, -6, 7, -8, 9, -10] |
| DiagCol2 | [1, -6, 24, -80, 240, -672, 1792, -4608, 11520, -28160] |
| DiagCol3 | [1, -12, 90, -540, 2835, -13608, 61236, -262440, 1082565, -4330260] |
| DiagCol4 | [1, -20, 240, -2240, 17920, -129024, 860160, -5406720, 32440320, -187432960] |
| DiagCol5 | [1, -30, 525, -7000, 78750, -787500, 7218750, -61875000, 502734375, -3910156250] |
| DiagCol6 | [1, -42, 1008, -18144, 272160, -3592512, 43110144, -480370176, 5043886848, -50438868480] |
| DiagCol7 | [1, -56, 1764, -41160, 792330, -13311144, 201885684, -2826399576, 37096494435, -461645264080] |
| DiagCol8 | [1, -72, 2880, -84480, 2027520, -42172416, 787218432, -13495173120, 215922769920, -3262832967680] |
| DiagCol9 | [1, -90, 4455, -160380, 4691115, -118216098, 2659862205, -54717165360, 1046465787510, -18836384175180] |
Abel: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, -2, -10, -18, -20, -10, 18, 70, 152, 270] |
| PolyRow4 | [0, 9, 8, -39, -144, -295, -456, -567, -544, -279] |
| PolyRow5 | [0, -4, 122, 348, 404, -100, -1554, -4228, -8152, -12996] |
| PolyRow6 | [0, -95, -428, 441, 4072, 10345, 16380, 16177, 976, -39663] |
| PolyRow7 | [0, 414, -1594, -11778, -20772, 110, 87954, 267246, 523832, 778878] |
| PolyRow8 | [0, 49, 18608, 18129, -145952, -565615, -1050096, -966287, 749504, 5347953] |
| PolyRow9 | [0, -10088, -26254, 475416, 1582372, 1133720, -5367978, -22062824, -47650744, -69401448] |
Abel:Inv Polynomial values as columns
| PolyCol | Seq |
|---|---|
| PolyCol0 | [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
| PolyCol1 | [1, 1, -1, -2, 9, -4, -95, 414, 49, -10088] |
| PolyCol2 | [1, 2, 0, -10, 8, 122, -428, -1594, 18608, -26254] |
| PolyCol3 | [1, 3, 3, -18, -39, 348, 441, -11778, 18129, 475416] |
| PolyCol4 | [1, 4, 8, -20, -144, 404, 4072, -20772, -145952, 1582372] |
| PolyCol5 | [1, 5, 15, -10, -295, -100, 10345, 110, -565615, 1133720] |
| PolyCol6 | [1, 6, 24, 18, -456, -1554, 16380, 87954, -1050096, -5367978] |
| PolyCol7 | [1, 7, 35, 70, -567, -4228, 16177, 267246, -966287, -22062824] |
| PolyCol8 | [1, 8, 48, 152, -544, -8152, 976, 523832, 749504, -47650744] |
| PolyCol9 | [1, 9, 63, 270, -279, -12996, -39663, 778878, 5347953, -69401448] |
[]
Abel:Rev Triangle view
| Row | Seq |
|---|---|
| Row0 | [1] |
| Row1 | [1, 0] |
| Row2 | [1, 2, 0] |
| Row3 | [1, 6, 9, 0] |
| Row4 | [1, 12, 48, 64, 0] |
| Row5 | [1, 20, 150, 500, 625, 0] |
| Row6 | [1, 30, 360, 2160, 6480, 7776, 0] |
| Row7 | [1, 42, 735, 6860, 36015, 100842, 117649, 0] |
| Row8 | [1, 56, 1344, 17920, 143360, 688128, 1835008, 2097152, 0] |
| Row9 | [1, 72, 2268, 40824, 459270, 3306744, 14880348, 38263752, 43046721, 0] |
Abel:Rev Triangles
| Flat | Seq |
|---|---|
| Triangle | [[1], [1, 0], [1, 2, 0], [1, 6, 9, 0], [1, 12, 48, 64, 0], [1, 20, 150, 500, 625, 0], [1, 30, 360, 2160, 6480, 7776, 0], [1, 42, 735, 6860, 36015, 100842, 117649, 0], [1, 56, 1344, 17920, 143360, 688128, 1835008, 2097152, 0], [1, 72, 2268, 40824, 459270, 3306744, 14880348, 38263752, 43046721, 0]] |
| RevTabl | [[1], [0, 1], [0, 2, 1], [0, 9, 6, 1], [0, 64, 48, 12, 1], [0, 625, 500, 150, 20, 1], [0, 7776, 6480, 2160, 360, 30, 1], [0, 117649, 100842, 36015, 6860, 735, 42, 1], [0, 2097152, 1835008, 688128, 143360, 17920, 1344, 56, 1], [0, 43046721, 38263752, 14880348, 3306744, 459270, 40824, 2268, 72, 1]] |
| AntiDiag | [[1], [1], [1, 0], [1, 2], [1, 6, 0], [1, 12, 9], [1, 20, 48, 0], [1, 30, 150, 64], [1, 42, 360, 500, 0], [1, 56, 735, 2160, 625]] |
| AccTabl | [[1], [1, 1], [1, 3, 3], [1, 7, 16, 16], [1, 13, 61, 125, 125], [1, 21, 171, 671, 1296, 1296], [1, 31, 391, 2551, 9031, 16807, 16807], [1, 43, 778, 7638, 43653, 144495, 262144, 262144], [1, 57, 1401, 19321, 162681, 850809, 2685817, 4782969, 4782969], [1, 73, 2341, 43165, 502435, 3809179, 18689527, 56953279, 100000000, 100000000]] |
| RevAccTabl | [[1], [1, 1], [3, 3, 1], [16, 16, 7, 1], [125, 125, 61, 13, 1], [1296, 1296, 671, 171, 21, 1], [16807, 16807, 9031, 2551, 391, 31, 1], [262144, 262144, 144495, 43653, 7638, 778, 43, 1], [4782969, 4782969, 2685817, 850809, 162681, 19321, 1401, 57, 1], [100000000, 100000000, 56953279, 18689527, 3809179, 502435, 43165, 2341, 73, 1]] |
| AccRevTabl | [[1], [0, 1], [0, 2, 3], [0, 9, 15, 16], [0, 64, 112, 124, 125], [0, 625, 1125, 1275, 1295, 1296], [0, 7776, 14256, 16416, 16776, 16806, 16807], [0, 117649, 218491, 254506, 261366, 262101, 262143, 262144], [0, 2097152, 3932160, 4620288, 4763648, 4781568, 4782912, 4782968, 4782969], [0, 43046721, 81310473, 96190821, 99497565, 99956835, 99997659, 99999927, 99999999, 100000000]] |
| DiffxTabl | [[1], [1, 0], [1, 4, 0], [1, 12, 27, 0], [1, 24, 144, 256, 0], [1, 40, 450, 2000, 3125, 0], [1, 60, 1080, 8640, 32400, 46656, 0], [1, 84, 2205, 27440, 180075, 605052, 823543, 0], [1, 112, 4032, 71680, 716800, 4128768, 12845056, 16777216, 0], [1, 144, 6804, 163296, 2296350, 19840464, 104162436, 306110016, 387420489, 0]] |
Abel:Rev Row sums
| Trait | Seq |
|---|---|
| RowSum | [1, 1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000] |
| EvenSum | [1, 1, 1, 10, 49, 776, 6841, 154400, 1979713, 58388608] |
| OddSum | [0, 0, 2, 6, 76, 520, 9966, 107744, 2803256, 41611392] |
| AltSum | [1, 1, -1, 4, -27, 256, -3125, 46656, -823543, 16777216] |
| AbsSum | [1, 1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000] |
| AccSum | [1, 2, 7, 40, 325, 3456, 45619, 720896, 13286025, 280000000] |
| AccRevSum | [1, 1, 5, 40, 425, 5616, 88837, 1638400, 34543665, 820000000] |
| DiagSum | [1, 1, 1, 3, 7, 22, 69, 245, 903, 3577] |
Abel:Rev Transforms
| Trans | Seq |
|---|---|
| RowLcm | [1, 1, 2, 18, 192, 7500, 38880, 7058940, 220200960, 12053081880] |
| RowGcd | [1, 1, 2, 3, 4, 5, 6, 7, 8, 9] |
| RowMax | [1, 1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721] |
| CentralE | [1, 2, 48, 2160, 143360] |
| CentralO | [1, 6, 150, 6860, 459270] |
| ColMiddle | [1, 1, 2, 6, 48, 150, 2160, 6860, 143360, 459270] |
| 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, 46, 593, 9726, 192637, 4457580, 117769409, 3492894070] |
| InvBinConv | [1, -1, -3, -10, -15, 474, 12565, 258572, 5136705, 102255290] |
| TransSqrs | [0, 0, 2, 42, 780, 15120, 318990, 7397376, 188484408, 5256000000] |
| TransNat0 | [0, 0, 2, 24, 300, 4320, 72030, 1376256, 29760696, 720000000] |
| TransNat1 | [1, 1, 5, 40, 425, 5616, 88837, 1638400, 34543665, 820000000] |
| PosHalf | [1, 2, 8, 50, 432, 4802, 65536, 1062882, 20000000, 428717762] |
| NegHalf | [1, -2, 0, -2, -16, -162, -2048, -31250, -559872, -11529602] |
Abel:Rev Diagonals as rows
| DiagRow | Seq |
|---|---|
| DiagRow0 | [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
| DiagRow1 | [1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000] |
| DiagRow2 | [1, 6, 48, 500, 6480, 100842, 1835008, 38263752, 900000000, 23579476910] |
| DiagRow3 | [1, 12, 150, 2160, 36015, 688128, 14880348, 360000000, 9646149645, 283787919360] |
| DiagRow4 | [1, 20, 360, 6860, 143360, 3306744, 84000000, 2338460520, 70946979840, 2332989862060] |
| DiagRow5 | [1, 30, 735, 17920, 459270, 12600000, 372027810, 11824496640, 403786706895, 14772648450560] |
| DiagRow6 | [1, 42, 1344, 40824, 1260000, 40584852, 1379524608, 49696825464, 1899340515072, 76963605468750] |
| DiagRow7 | [1, 56, 2268, 84000, 3074610, 114960384, 4459971516, 180889572864, 7696360546875, 343940981063680] |
| DiagRow8 | [1, 72, 3600, 159720, 6842880, 294064056, 12920683776, 586389375000, 27638114549760, 1356645307125680] |
| DiagRow9 | [1, 90, 5445, 285120, 14137695, 692179488, 34206046875, 1727382159360, 89777998265670, 4822114348846080] |
Abel: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, 9, 48, 150, 360, 735, 1344, 2268, 3600, 5445] |
| DiagCol3 | [0, 64, 500, 2160, 6860, 17920, 40824, 84000, 159720, 285120] |
| DiagCol4 | [0, 625, 6480, 36015, 143360, 459270, 1260000, 3074610, 6842880, 14137695] |
| DiagCol5 | [0, 7776, 100842, 688128, 3306744, 12600000, 40584852, 114960384, 294064056, 692179488] |
| DiagCol6 | [0, 117649, 1835008, 14880348, 84000000, 372027810, 1379524608, 4459971516, 12920683776, 34206046875] |
| DiagCol7 | [0, 2097152, 38263752, 360000000, 2338460520, 11824496640, 49696825464, 180889572864, 586389375000, 1727382159360] |
| DiagCol8 | [0, 43046721, 900000000, 9646149645, 70946979840, 403786706895, 1899340515072, 7696360546875, 27638114549760, 89777998265670] |
| DiagCol9 | [0, 1000000000, 23579476910, 283787919360, 2332989862060, 14772648450560, 76963605468750, 343940981063680, 1356645307125680, 4822114348846080] |
Abel: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, 16, 49, 100, 169, 256, 361, 484, 625, 784] |
| PolyRow4 | [1, 125, 729, 2197, 4913, 9261, 15625, 24389, 35937, 50653] |
| PolyRow5 | [1, 1296, 14641, 65536, 194481, 456976, 923521, 1679616, 2825761, 4477456] |
| PolyRow6 | [1, 16807, 371293, 2476099, 9765625, 28629151, 69343957, 147008443, 282475249, 503284375] |
| PolyRow7 | [1, 262144, 11390625, 113379904, 594823321, 2176782336, 6321363049, 15625000000, 34296447249, 68719476736] |
| PolyRow8 | [1, 4782969, 410338673, 6103515625, 42618442977, 194754273881, 678223072849, 1954897493193, 4902227890625, 11047398519097] |
| PolyRow9 | [1, 100000000, 16983563041, 377801998336, 3512479453921, 20047612231936, 83733937890625, 281474976710656, 806460091894081, 2044140858654976] |
Abel:Rev Polynomial values as columns
| PolyCol | Seq |
|---|---|
| PolyCol0 | [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] |
| PolyCol1 | [1, 1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000] |
| PolyCol2 | [1, 1, 5, 49, 729, 14641, 371293, 11390625, 410338673, 16983563041] |
| PolyCol3 | [1, 1, 7, 100, 2197, 65536, 2476099, 113379904, 6103515625, 377801998336] |
| PolyCol4 | [1, 1, 9, 169, 4913, 194481, 9765625, 594823321, 42618442977, 3512479453921] |
| PolyCol5 | [1, 1, 11, 256, 9261, 456976, 28629151, 2176782336, 194754273881, 20047612231936] |
| PolyCol6 | [1, 1, 13, 361, 15625, 923521, 69343957, 6321363049, 678223072849, 83733937890625] |
| PolyCol7 | [1, 1, 15, 484, 24389, 1679616, 147008443, 15625000000, 1954897493193, 281474976710656] |
| PolyCol8 | [1, 1, 17, 625, 35937, 2825761, 282475249, 34296447249, 4902227890625, 806460091894081] |
| PolyCol9 | [1, 1, 19, 784, 50653, 4477456, 503284375, 68719476736, 11047398519097, 2044140858654976] |
[]
Abel:Inv:Rev Triangle view
| Row | Seq |
|---|---|
| Row0 | [1] |
| Row1 | [1, 0] |
| Row2 | [1, -2, 0] |
| Row3 | [1, -6, 3, 0] |
| Row4 | [1, -12, 24, -4, 0] |
| Row5 | [1, -20, 90, -80, 5, 0] |
| Row6 | [1, -30, 240, -540, 240, -6, 0] |
| Row7 | [1, -42, 525, -2240, 2835, -672, 7, 0] |
| Row8 | [1, -56, 1008, -7000, 17920, -13608, 1792, -8, 0] |
| Row9 | [1, -72, 1764, -18144, 78750, -129024, 61236, -4608, 9, 0] |
Abel:Inv:Rev Triangles
| Flat | Seq |
|---|---|
| Triangle | [[1], [1, 0], [1, -2, 0], [1, -6, 3, 0], [1, -12, 24, -4, 0], [1, -20, 90, -80, 5, 0], [1, -30, 240, -540, 240, -6, 0], [1, -42, 525, -2240, 2835, -672, 7, 0], [1, -56, 1008, -7000, 17920, -13608, 1792, -8, 0], [1, -72, 1764, -18144, 78750, -129024, 61236, -4608, 9, 0]] |
| RevTabl | [[1], [0, 1], [0, -2, 1], [0, 3, -6, 1], [0, -4, 24, -12, 1], [0, 5, -80, 90, -20, 1], [0, -6, 240, -540, 240, -30, 1], [0, 7, -672, 2835, -2240, 525, -42, 1], [0, -8, 1792, -13608, 17920, -7000, 1008, -56, 1], [0, 9, -4608, 61236, -129024, 78750, -18144, 1764, -72, 1]] |
| AntiDiag | [[1], [1], [1, 0], [1, -2], [1, -6, 0], [1, -12, 3], [1, -20, 24, 0], [1, -30, 90, -4], [1, -42, 240, -80, 0], [1, -56, 525, -540, 5]] |
| AccTabl | [[1], [1, 1], [1, -1, -1], [1, -5, -2, -2], [1, -11, 13, 9, 9], [1, -19, 71, -9, -4, -4], [1, -29, 211, -329, -89, -95, -95], [1, -41, 484, -1756, 1079, 407, 414, 414], [1, -55, 953, -6047, 11873, -1735, 57, 49, 49], [1, -71, 1693, -16451, 62299, -66725, -5489, -10097, -10088, -10088]] |
| RevAccTabl | [[1], [1, 1], [-1, -1, 1], [-2, -2, -5, 1], [9, 9, 13, -11, 1], [-4, -4, -9, 71, -19, 1], [-95, -95, -89, -329, 211, -29, 1], [414, 414, 407, 1079, -1756, 484, -41, 1], [49, 49, 57, -1735, 11873, -6047, 953, -55, 1], [-10088, -10088, -10097, -5489, -66725, 62299, -16451, 1693, -71, 1]] |
| AccRevTabl | [[1], [0, 1], [0, -2, -1], [0, 3, -3, -2], [0, -4, 20, 8, 9], [0, 5, -75, 15, -5, -4], [0, -6, 234, -306, -66, -96, -95], [0, 7, -665, 2170, -70, 455, 413, 414], [0, -8, 1784, -11824, 6096, -904, 104, 48, 49], [0, 9, -4599, 56637, -72387, 6363, -11781, -10017, -10089, -10088]] |
| DiffxTabl | [[1], [1, 0], [1, -4, 0], [1, -12, 9, 0], [1, -24, 72, -16, 0], [1, -40, 270, -320, 25, 0], [1, -60, 720, -2160, 1200, -36, 0], [1, -84, 1575, -8960, 14175, -4032, 49, 0], [1, -112, 3024, -28000, 89600, -81648, 12544, -64, 0], [1, -144, 5292, -72576, 393750, -774144, 428652, -36864, 81, 0]] |
Abel:Inv:Rev Row sums
| Trait | Seq |
|---|---|
| RowSum | [1, 1, -1, -2, 9, -4, -95, 414, 49, -10088] |
| EvenSum | [1, 1, 1, 4, 25, 96, 481, 3368, 20721, 141760] |
| OddSum | [0, 0, -2, -6, -16, -100, -576, -2954, -20672, -151848] |
| AltSum | [1, 1, 3, 10, 41, 196, 1057, 6322, 41393, 293608] |
| AbsSum | [1, 1, 3, 10, 41, 196, 1057, 6322, 41393, 293608] |
| AccSum | [1, 2, -1, -8, 21, 36, -425, 1002, 5145, -55016] |
| AccRevSum | [1, 1, -3, -2, 33, -64, -335, 2724, -4655, -55952] |
| DiagSum | [1, 1, 1, -1, -5, -8, 5, 57, 119, -65] |
Abel:Inv:Rev Transforms
| Trans | Seq |
|---|---|
| RowLcm | [1, 1, 2, 6, 24, 720, 2160, 907200, 108864000, 137168640000] |
| RowGcd | [1, 1, 2, 3, 4, 5, 6, 7, 8, 9] |
| RowMax | [1, 1, 2, 6, 24, 90, 540, 2835, 17920, 129024] |
| CentralE | [1, -2, 24, -540, 17920] |
| CentralO | [1, -6, 90, -2240, 78750] |
| ColMiddle | [1, 1, -2, -6, 24, 90, -540, -2240, 17920, 78750] |
| 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, -8, 81, 26, -3815, 17494, 178241, -2817746] |
| InvBinConv | [1, -1, 5, -28, 209, -1826, 18217, -203106, 2487361, -33077566] |
| TransSqrs | [0, 0, -2, 6, 48, -300, -240, 10710, -48384, -142632] |
| TransNat0 | [0, 0, -2, 0, 24, -60, -240, 2310, -4704, -45864] |
| TransNat1 | [1, 1, -3, -2, 33, -64, -335, 2724, -4655, -55952] |
| PosHalf | [1, 2, 0, -10, 8, 122, -428, -1594, 18608, -26254] |
| NegHalf | [1, -2, 8, -38, 216, -1402, 10156, -80838, 698704, -6498674] |
Abel:Inv:Rev Diagonals as rows
| DiagRow | Seq |
|---|---|
| DiagRow0 | [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
| DiagRow1 | [1, -2, 3, -4, 5, -6, 7, -8, 9, -10] |
| DiagRow2 | [1, -6, 24, -80, 240, -672, 1792, -4608, 11520, -28160] |
| DiagRow3 | [1, -12, 90, -540, 2835, -13608, 61236, -262440, 1082565, -4330260] |
| DiagRow4 | [1, -20, 240, -2240, 17920, -129024, 860160, -5406720, 32440320, -187432960] |
| DiagRow5 | [1, -30, 525, -7000, 78750, -787500, 7218750, -61875000, 502734375, -3910156250] |
| DiagRow6 | [1, -42, 1008, -18144, 272160, -3592512, 43110144, -480370176, 5043886848, -50438868480] |
| DiagRow7 | [1, -56, 1764, -41160, 792330, -13311144, 201885684, -2826399576, 37096494435, -461645264080] |
| DiagRow8 | [1, -72, 2880, -84480, 2027520, -42172416, 787218432, -13495173120, 215922769920, -3262832967680] |
| DiagRow9 | [1, -90, 4455, -160380, 4691115, -118216098, 2659862205, -54717165360, 1046465787510, -18836384175180] |
Abel: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, 3, 24, 90, 240, 525, 1008, 1764, 2880, 4455] |
| DiagCol3 | [0, -4, -80, -540, -2240, -7000, -18144, -41160, -84480, -160380] |
| DiagCol4 | [0, 5, 240, 2835, 17920, 78750, 272160, 792330, 2027520, 4691115] |
| DiagCol5 | [0, -6, -672, -13608, -129024, -787500, -3592512, -13311144, -42172416, -118216098] |
| DiagCol6 | [0, 7, 1792, 61236, 860160, 7218750, 43110144, 201885684, 787218432, 2659862205] |
| DiagCol7 | [0, -8, -4608, -262440, -5406720, -61875000, -480370176, -2826399576, -13495173120, -54717165360] |
| DiagCol8 | [0, 9, 11520, 1082565, 32440320, 502734375, 5043886848, 37096494435, 215922769920, 1046465787510] |
| DiagCol9 | [0, -10, -28160, -4330260, -187432960, -3910156250, -50438868480, -461645264080, -3262832967680, -18836384175180] |
Abel: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, -2, 1, 10, 25, 46, 73, 106, 145, 190] |
| PolyRow4 | [1, 9, 41, 73, 81, 41, -71, -279, -607, -1079] |
| PolyRow5 | [1, -4, -239, -1004, -2479, -4724, -7679, -11164, -14879, -18404] |
| PolyRow6 | [1, -95, 229, 5473, 24457, 69601, 156205, 301729, 525073, 845857] |
| PolyRow7 | [1, 414, 8401, 15562, -68823, -485834, -1689911, -4406814, -9686543, -18951218] |
| PolyRow8 | [1, 49, -87151, -746447, -2570207, -4800079, -2699471, 16202929, 76958273, 223090993] |
| PolyRow9 | [1, -10088, 324577, 9174088, 62821153, 244122616, 677111617, 1475786152, 2625492673, 3775676248] |
Abel:Inv:Rev Polynomial values as columns
| PolyCol | Seq |
|---|---|
| PolyCol0 | [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] |
| PolyCol1 | [1, 1, -1, -2, 9, -4, -95, 414, 49, -10088] |
| PolyCol2 | [1, 1, -3, 1, 41, -239, 229, 8401, -87151, 324577] |
| PolyCol3 | [1, 1, -5, 10, 73, -1004, 5473, 15562, -746447, 9174088] |
| PolyCol4 | [1, 1, -7, 25, 81, -2479, 24457, -68823, -2570207, 62821153] |
| PolyCol5 | [1, 1, -9, 46, 41, -4724, 69601, -485834, -4800079, 244122616] |
| PolyCol6 | [1, 1, -11, 73, -71, -7679, 156205, -1689911, -2699471, 677111617] |
| PolyCol7 | [1, 1, -13, 106, -279, -11164, 301729, -4406814, 16202929, 1475786152] |
| PolyCol8 | [1, 1, -15, 145, -607, -14879, 525073, -9686543, 76958273, 2625492673] |
| PolyCol9 | [1, 1, -17, 190, -1079, -18404, 845857, -18951218, 223090993, 3775676248] |