['A038719']
Chains Triangle view
Row | Seq |
---|---|
Row0 | [1] |
Row1 | [2, 1] |
Row2 | [4, 5, 2] |
Row3 | [8, 19, 18, 6] |
Row4 | [16, 65, 110, 84, 24] |
Row5 | [32, 211, 570, 750, 480, 120] |
Row6 | [64, 665, 2702, 5460, 5880, 3240, 720] |
Row7 | [128, 2059, 12138, 35406, 57120, 52080, 25200, 5040] |
Row8 | [256, 6305, 52670, 213444, 484344, 650160, 514080, 221760, 40320] |
Row9 | [512, 19171, 223290, 1225230, 3759840, 6972840, 8013600, 5594400, 2177280, 362880] |
Chains Triangles
Flat | Seq |
---|---|
Triangle | [[1], [2, 1], [4, 5, 2], [8, 19, 18, 6], [16, 65, 110, 84, 24], [32, 211, 570, 750, 480, 120], [64, 665, 2702, 5460, 5880, 3240, 720], [128, 2059, 12138, 35406, 57120, 52080, 25200, 5040], [256, 6305, 52670, 213444, 484344, 650160, 514080, 221760, 40320], [512, 19171, 223290, 1225230, 3759840, 6972840, 8013600, 5594400, 2177280, 362880]] |
RevTabl | [[1], [1, 2], [2, 5, 4], [6, 18, 19, 8], [24, 84, 110, 65, 16], [120, 480, 750, 570, 211, 32], [720, 3240, 5880, 5460, 2702, 665, 64], [5040, 25200, 52080, 57120, 35406, 12138, 2059, 128], [40320, 221760, 514080, 650160, 484344, 213444, 52670, 6305, 256], [362880, 2177280, 5594400, 8013600, 6972840, 3759840, 1225230, 223290, 19171, 512]] |
AntiDiag | [[1], [2], [4, 1], [8, 5], [16, 19, 2], [32, 65, 18], [64, 211, 110, 6], [128, 665, 570, 84], [256, 2059, 2702, 750, 24], [512, 6305, 12138, 5460, 480]] |
AccTabl | [[1], [2, 3], [4, 9, 11], [8, 27, 45, 51], [16, 81, 191, 275, 299], [32, 243, 813, 1563, 2043, 2163], [64, 729, 3431, 8891, 14771, 18011, 18731], [128, 2187, 14325, 49731, 106851, 158931, 184131, 189171], [256, 6561, 59231, 272675, 757019, 1407179, 1921259, 2143019, 2183339], [512, 19683, 242973, 1468203, 5228043, 12200883, 20214483, 25808883, 27986163, 28349043]] |
RevAccTabl | [[1], [3, 2], [11, 9, 4], [51, 45, 27, 8], [299, 275, 191, 81, 16], [2163, 2043, 1563, 813, 243, 32], [18731, 18011, 14771, 8891, 3431, 729, 64], [189171, 184131, 158931, 106851, 49731, 14325, 2187, 128], [2183339, 2143019, 1921259, 1407179, 757019, 272675, 59231, 6561, 256], [28349043, 27986163, 25808883, 20214483, 12200883, 5228043, 1468203, 242973, 19683, 512]] |
AccRevTabl | [[1], [1, 3], [2, 7, 11], [6, 24, 43, 51], [24, 108, 218, 283, 299], [120, 600, 1350, 1920, 2131, 2163], [720, 3960, 9840, 15300, 18002, 18667, 18731], [5040, 30240, 82320, 139440, 174846, 186984, 189043, 189171], [40320, 262080, 776160, 1426320, 1910664, 2124108, 2176778, 2183083, 2183339], [362880, 2540160, 8134560, 16148160, 23121000, 26880840, 28106070, 28329360, 28348531, 28349043]] |
DiffxTabl | [[1], [2, 2], [4, 10, 6], [8, 38, 54, 24], [16, 130, 330, 336, 120], [32, 422, 1710, 3000, 2400, 720], [64, 1330, 8106, 21840, 29400, 19440, 5040], [128, 4118, 36414, 141624, 285600, 312480, 176400, 40320], [256, 12610, 158010, 853776, 2421720, 3900960, 3598560, 1774080, 362880], [512, 38342, 669870, 4900920, 18799200, 41837040, 56095200, 44755200, 19595520, 3628800]] |
Chains Row sums
Trait | Seq |
---|---|
RowSum | [1, 3, 11, 51, 299, 2163, 18731, 189171, 2183339, 28349043] |
EvenSum | [1, 2, 6, 26, 150, 1082, 9366, 94586, 1091670, 14174522] |
OddSum | [0, 1, 5, 25, 149, 1081, 9365, 94585, 1091669, 14174521] |
AltSum | [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] |
AbsSum | [1, 3, 11, 51, 299, 2163, 18731, 189171, 2183339, 28349043] |
AccSum | [1, 5, 24, 131, 862, 6857, 64628, 705455, 8750538, 121518869] |
AccRevSum | [1, 4, 20, 124, 932, 8284, 85220, 997084, 13082852, 190320604] |
DiagSum | [1, 2, 5, 13, 37, 115, 391, 1447, 5791, 24895] |
Chains Transforms
Trans | Seq |
---|---|
RowLcm | [1, 2, 20, 1368, 240240, 48108000, 60545983680, 1044991435017600, 956036236766889358080, 28533596267289599817705561600] |
RowGcd | [1, 2, 1, 1, 1, 1, 1, 1, 1, 1] |
RowMax | [1, 2, 5, 19, 110, 750, 5880, 57120, 650160, 8013600] |
CentralE | [1, 5, 110, 5460, 484344] |
CentralO | [2, 19, 570, 35406, 3759840] |
ColMiddle | [1, 2, 5, 19, 110, 570, 5460, 35406, 484344, 3759840] |
ColLeft | [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] |
ColRight | [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880] |
BinConv | [1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000, 2357947691] |
InvBinConv | [1, -1, -4, 1, 104, 543, -3116, -78283, -372688, 8914267] |
TransSqrs | [0, 1, 13, 145, 1645, 19921, 261613, 3739345, 58095085, 977772241] |
TransNat0 | [0, 1, 9, 73, 633, 6121, 66489, 807913, 10899513, 161971561] |
TransNat1 | [1, 4, 20, 124, 932, 8284, 85220, 997084, 13082852, 190320604] |
PosHalf | [1, 5, 28, 182, 1408, 13040, 143008, 1823792, 26564608, 435249920] |
NegHalf | [1, -3, 8, -18, 32, -48, 128, -528, 512, 6912] |
Chains Diagonals as rows
DiagRow | Seq |
---|---|
DiagRow0 | [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880] |
DiagRow1 | [2, 5, 18, 84, 480, 3240, 25200, 221760, 2177280, 23587200] |
DiagRow2 | [4, 19, 110, 750, 5880, 52080, 514080, 5594400, 66528000, 858211200] |
DiagRow3 | [8, 65, 570, 5460, 57120, 650160, 8013600, 106444800, 1516838400, 23091868800] |
DiagRow4 | [16, 211, 2702, 35406, 484344, 6972840, 105945840, 1699624080, 28765376640, 512898946560] |
DiagRow5 | [32, 665, 12138, 213444, 3759840, 67609080, 1253221200, 24069165120, 480207087360, 9963752198400] |
DiagRow6 | [64, 2059, 52670, 1225230, 27459960, 610563360, 13689149760, 312446534400, 7301643148800, 175316062521600] |
DiagRow7 | [128, 6305, 223290, 6796020, 191943840, 5233662720, 140915174400, 3798425030400, 103403831731200, 2859111173318400] |
DiagRow8 | [256, 19171, 931502, 36774606, 1298761464, 43129446360, 1386098073360, 43888511787120, 1385146411608960, 43916540610983040] |
DiagRow9 | [512, 58025, 3842058, 195399204, 8574165600, 344776952520, 13157446302000, 487098730198080, 17748253957674240, 642816232339881600] |
Chains Diagonals as columns
DiagCol | Seq |
---|---|
DiagCol0 | [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] |
DiagCol1 | [1, 5, 19, 65, 211, 665, 2059, 6305, 19171, 58025] |
DiagCol2 | [2, 18, 110, 570, 2702, 12138, 52670, 223290, 931502, 3842058] |
DiagCol3 | [6, 84, 750, 5460, 35406, 213444, 1225230, 6796020, 36774606, 195399204] |
DiagCol4 | [24, 480, 5880, 57120, 484344, 3759840, 27459960, 191943840, 1298761464, 8574165600] |
DiagCol5 | [120, 3240, 52080, 650160, 6972840, 67609080, 610563360, 5233662720, 43129446360, 344776952520] |
DiagCol6 | [720, 25200, 514080, 8013600, 105945840, 1253221200, 13689149760, 140915174400, 1386098073360, 13157446302000] |
DiagCol7 | [5040, 221760, 5594400, 106444800, 1699624080, 24069165120, 312446534400, 3798425030400, 43888511787120, 487098730198080] |
DiagCol8 | [40320, 2177280, 66528000, 1516838400, 28765376640, 480207087360, 7301643148800, 103403831731200, 1385146411608960, 17748253957674240] |
DiagCol9 | [362880, 23587200, 858211200, 23091868800, 512898946560, 9963752198400, 175316062521600, 2859111173318400, 43916540610983040, 642816232339881600] |
Chains Polynomial values as rows
PolyRow | Seq |
---|---|
PolyRow0 | [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] |
PolyRow1 | [2, 3, 4, 5, 6, 7, 8, 9, 10, 11] |
PolyRow2 | [4, 11, 22, 37, 56, 79, 106, 137, 172, 211] |
PolyRow3 | [8, 51, 166, 389, 756, 1303, 2066, 3081, 4384, 6011] |
PolyRow4 | [16, 299, 1642, 5413, 13556, 28591, 53614, 92297, 148888, 228211] |
PolyRow5 | [32, 2163, 20254, 94085, 303756, 784087, 1739018, 3456009, 6320440, 10830011] |
PolyRow6 | [64, 18731, 299722, 1962277, 8167556, 25803439, 67687726, 155289737, 321970312, 616740211] |
PolyRow7 | [128, 189171, 5174446, 47746949, 256215756, 990689623, 3073707386, 8140618761, 19135117144, 40975326011] |
PolyRow8 | [256, 2183339, 102094042, 1327769893, 9185683556, 43469994031, 159517033054, 487712655497, 1299685784968, 3111247188211] |
PolyRow9 | [512, 28349043, 2266154014, 41538664325, 370484163756, 2145823857367, 9313311489098, 32871775042569, 99311178384280, 265765828110011] |
Chains Polynomial values as columns
PolyCol | Seq |
---|---|
PolyCol0 | [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] |
PolyCol1 | [1, 3, 11, 51, 299, 2163, 18731, 189171, 2183339, 28349043] |
PolyCol2 | [1, 4, 22, 166, 1642, 20254, 299722, 5174446, 102094042, 2266154014] |
PolyCol3 | [1, 5, 37, 389, 5413, 94085, 1962277, 47746949, 1327769893, 41538664325] |
PolyCol4 | [1, 6, 56, 756, 13556, 303756, 8167556, 256215756, 9185683556, 370484163756] |
PolyCol5 | [1, 7, 79, 1303, 28591, 784087, 25803439, 990689623, 43469994031, 2145823857367] |
PolyCol6 | [1, 8, 106, 2066, 53614, 1739018, 67687726, 3073707386, 159517033054, 9313311489098] |
PolyCol7 | [1, 9, 137, 3081, 92297, 3456009, 155289737, 8140618761, 487712655497, 32871775042569] |
PolyCol8 | [1, 10, 172, 4384, 148888, 6320440, 321970312, 19135117144, 1299685784968, 99311178384280] |
PolyCol9 | [1, 11, 211, 6011, 228211, 10830011, 616740211, 40975326011, 3111247188211, 265765828110011] |
[]
Chains:Rev Triangle view
Row | Seq |
---|---|
Row0 | [1] |
Row1 | [1, 2] |
Row2 | [2, 5, 4] |
Row3 | [6, 18, 19, 8] |
Row4 | [24, 84, 110, 65, 16] |
Row5 | [120, 480, 750, 570, 211, 32] |
Row6 | [720, 3240, 5880, 5460, 2702, 665, 64] |
Row7 | [5040, 25200, 52080, 57120, 35406, 12138, 2059, 128] |
Row8 | [40320, 221760, 514080, 650160, 484344, 213444, 52670, 6305, 256] |
Row9 | [362880, 2177280, 5594400, 8013600, 6972840, 3759840, 1225230, 223290, 19171, 512] |
Chains:Rev Triangles
Flat | Seq |
---|---|
Triangle | [[1], [1, 2], [2, 5, 4], [6, 18, 19, 8], [24, 84, 110, 65, 16], [120, 480, 750, 570, 211, 32], [720, 3240, 5880, 5460, 2702, 665, 64], [5040, 25200, 52080, 57120, 35406, 12138, 2059, 128], [40320, 221760, 514080, 650160, 484344, 213444, 52670, 6305, 256], [362880, 2177280, 5594400, 8013600, 6972840, 3759840, 1225230, 223290, 19171, 512]] |
RevTabl | [[1], [2, 1], [4, 5, 2], [8, 19, 18, 6], [16, 65, 110, 84, 24], [32, 211, 570, 750, 480, 120], [64, 665, 2702, 5460, 5880, 3240, 720], [128, 2059, 12138, 35406, 57120, 52080, 25200, 5040], [256, 6305, 52670, 213444, 484344, 650160, 514080, 221760, 40320], [512, 19171, 223290, 1225230, 3759840, 6972840, 8013600, 5594400, 2177280, 362880]] |
AntiDiag | [[1], [1], [2, 2], [6, 5], [24, 18, 4], [120, 84, 19], [720, 480, 110, 8], [5040, 3240, 750, 65], [40320, 25200, 5880, 570, 16], [362880, 221760, 52080, 5460, 211]] |
AccTabl | [[1], [1, 3], [2, 7, 11], [6, 24, 43, 51], [24, 108, 218, 283, 299], [120, 600, 1350, 1920, 2131, 2163], [720, 3960, 9840, 15300, 18002, 18667, 18731], [5040, 30240, 82320, 139440, 174846, 186984, 189043, 189171], [40320, 262080, 776160, 1426320, 1910664, 2124108, 2176778, 2183083, 2183339], [362880, 2540160, 8134560, 16148160, 23121000, 26880840, 28106070, 28329360, 28348531, 28349043]] |
RevAccTabl | [[1], [3, 1], [11, 7, 2], [51, 43, 24, 6], [299, 283, 218, 108, 24], [2163, 2131, 1920, 1350, 600, 120], [18731, 18667, 18002, 15300, 9840, 3960, 720], [189171, 189043, 186984, 174846, 139440, 82320, 30240, 5040], [2183339, 2183083, 2176778, 2124108, 1910664, 1426320, 776160, 262080, 40320], [28349043, 28348531, 28329360, 28106070, 26880840, 23121000, 16148160, 8134560, 2540160, 362880]] |
AccRevTabl | [[1], [2, 3], [4, 9, 11], [8, 27, 45, 51], [16, 81, 191, 275, 299], [32, 243, 813, 1563, 2043, 2163], [64, 729, 3431, 8891, 14771, 18011, 18731], [128, 2187, 14325, 49731, 106851, 158931, 184131, 189171], [256, 6561, 59231, 272675, 757019, 1407179, 1921259, 2143019, 2183339], [512, 19683, 242973, 1468203, 5228043, 12200883, 20214483, 25808883, 27986163, 28349043]] |
DiffxTabl | [[1], [1, 4], [2, 10, 12], [6, 36, 57, 32], [24, 168, 330, 260, 80], [120, 960, 2250, 2280, 1055, 192], [720, 6480, 17640, 21840, 13510, 3990, 448], [5040, 50400, 156240, 228480, 177030, 72828, 14413, 1024], [40320, 443520, 1542240, 2600640, 2421720, 1280664, 368690, 50440, 2304], [362880, 4354560, 16783200, 32054400, 34864200, 22559040, 8576610, 1786320, 172539, 5120]] |
Chains:Rev Row sums
Trait | Seq |
---|---|
RowSum | [1, 3, 11, 51, 299, 2163, 18731, 189171, 2183339, 28349043] |
EvenSum | [1, 1, 6, 25, 150, 1081, 9366, 94585, 1091670, 14174521] |
OddSum | [0, 2, 5, 26, 149, 1082, 9365, 94586, 1091669, 14174522] |
AltSum | [1, -1, 1, -1, 1, -1, 1, -1, 1, -1] |
AbsSum | [1, 3, 11, 51, 299, 2163, 18731, 189171, 2183339, 28349043] |
AccSum | [1, 4, 20, 124, 932, 8284, 85220, 997084, 13082852, 190320604] |
AccRevSum | [1, 5, 24, 131, 862, 6857, 64628, 705455, 8750538, 121518869] |
DiagSum | [1, 1, 4, 11, 46, 223, 1318, 9095, 71986, 642391] |
Chains:Rev Transforms
Trans | Seq |
---|---|
RowLcm | [1, 2, 20, 1368, 240240, 48108000, 60545983680, 1044991435017600, 956036236766889358080, 28533596267289599817705561600] |
RowGcd | [1, 2, 1, 1, 1, 1, 1, 1, 1, 1] |
RowMax | [1, 2, 5, 19, 110, 750, 5880, 57120, 650160, 8013600] |
CentralE | [1, 5, 110, 5460, 484344] |
CentralO | [1, 18, 750, 57120, 6972840] |
ColMiddle | [1, 1, 5, 18, 110, 750, 5460, 57120, 484344, 6972840] |
ColLeft | [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880] |
ColRight | [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] |
BinConv | [1, 3, 16, 125, 1296, 16807, 262144, 4782969, 100000000, 2357947691] |
InvBinConv | [1, 1, -4, -1, 104, -543, -3116, 78283, -372688, -8914267] |
TransSqrs | [0, 2, 21, 166, 1365, 12786, 138061, 1697942, 23436573, 358556626] |
TransNat0 | [0, 2, 13, 80, 563, 4694, 45897, 516284, 6567199, 93169826] |
TransNat1 | [1, 5, 24, 131, 862, 6857, 64628, 705455, 8750538, 121518869] |
PosHalf | [1, 4, 22, 166, 1642, 20254, 299722, 5174446, 102094042, 2266154014] |
NegHalf | [1, 0, 2, -6, 38, -270, 2342, -23646, 272918, -3543630] |
Chains:Rev Diagonals as rows
DiagRow | Seq |
---|---|
DiagRow0 | [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] |
DiagRow1 | [1, 5, 19, 65, 211, 665, 2059, 6305, 19171, 58025] |
DiagRow2 | [2, 18, 110, 570, 2702, 12138, 52670, 223290, 931502, 3842058] |
DiagRow3 | [6, 84, 750, 5460, 35406, 213444, 1225230, 6796020, 36774606, 195399204] |
DiagRow4 | [24, 480, 5880, 57120, 484344, 3759840, 27459960, 191943840, 1298761464, 8574165600] |
DiagRow5 | [120, 3240, 52080, 650160, 6972840, 67609080, 610563360, 5233662720, 43129446360, 344776952520] |
DiagRow6 | [720, 25200, 514080, 8013600, 105945840, 1253221200, 13689149760, 140915174400, 1386098073360, 13157446302000] |
DiagRow7 | [5040, 221760, 5594400, 106444800, 1699624080, 24069165120, 312446534400, 3798425030400, 43888511787120, 487098730198080] |
DiagRow8 | [40320, 2177280, 66528000, 1516838400, 28765376640, 480207087360, 7301643148800, 103403831731200, 1385146411608960, 17748253957674240] |
DiagRow9 | [362880, 23587200, 858211200, 23091868800, 512898946560, 9963752198400, 175316062521600, 2859111173318400, 43916540610983040, 642816232339881600] |
Chains:Rev Diagonals as columns
DiagCol | Seq |
---|---|
DiagCol0 | [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880] |
DiagCol1 | [2, 5, 18, 84, 480, 3240, 25200, 221760, 2177280, 23587200] |
DiagCol2 | [4, 19, 110, 750, 5880, 52080, 514080, 5594400, 66528000, 858211200] |
DiagCol3 | [8, 65, 570, 5460, 57120, 650160, 8013600, 106444800, 1516838400, 23091868800] |
DiagCol4 | [16, 211, 2702, 35406, 484344, 6972840, 105945840, 1699624080, 28765376640, 512898946560] |
DiagCol5 | [32, 665, 12138, 213444, 3759840, 67609080, 1253221200, 24069165120, 480207087360, 9963752198400] |
DiagCol6 | [64, 2059, 52670, 1225230, 27459960, 610563360, 13689149760, 312446534400, 7301643148800, 175316062521600] |
DiagCol7 | [128, 6305, 223290, 6796020, 191943840, 5233662720, 140915174400, 3798425030400, 103403831731200, 2859111173318400] |
DiagCol8 | [256, 19171, 931502, 36774606, 1298761464, 43129446360, 1386098073360, 43888511787120, 1385146411608960, 43916540610983040] |
DiagCol9 | [512, 58025, 3842058, 195399204, 8574165600, 344776952520, 13157446302000, 487098730198080, 17748253957674240, 642816232339881600] |
Chains:Rev Polynomial values as rows
PolyRow | Seq |
---|---|
PolyRow0 | [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] |
PolyRow1 | [1, 3, 5, 7, 9, 11, 13, 15, 17, 19] |
PolyRow2 | [2, 11, 28, 53, 86, 127, 176, 233, 298, 371] |
PolyRow3 | [6, 51, 182, 447, 894, 1571, 2526, 3807, 5462, 7539] |
PolyRow4 | [24, 299, 1408, 4317, 10376, 21319, 39264, 66713, 106552, 162051] |
PolyRow5 | [120, 2163, 13040, 48567, 137304, 324395, 675408, 1280175, 2256632, 3754659] |
PolyRow6 | [720, 18731, 143008, 637893, 2092016, 5613295, 13070016, 27377993, 52833808, 95494131] |
PolyRow7 | [5040, 189171, 1823792, 9689967, 36618864, 110804915, 286536816, 658991487, 1383736112, 2701583379] |
PolyRow8 | [40320, 2183339, 26564608, 167850477, 729136256, 2480545495, 7100112384, 17864851193, 40670238592, 85466656611] |
PolyRow9 | [362880, 28349043, 435249920, 3269439207, 16314109824, 62337756155, 197250018048, 542185861455, 1336057223552, 3016813197699] |
Chains:Rev Polynomial values as columns
PolyCol | Seq |
---|---|
PolyCol0 | [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880] |
PolyCol1 | [1, 3, 11, 51, 299, 2163, 18731, 189171, 2183339, 28349043] |
PolyCol2 | [1, 5, 28, 182, 1408, 13040, 143008, 1823792, 26564608, 435249920] |
PolyCol3 | [1, 7, 53, 447, 4317, 48567, 637893, 9689967, 167850477, 3269439207] |
PolyCol4 | [1, 9, 86, 894, 10376, 137304, 2092016, 36618864, 729136256, 16314109824] |
PolyCol5 | [1, 11, 127, 1571, 21319, 324395, 5613295, 110804915, 2480545495, 62337756155] |
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