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A137320
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A triangular sequence from a coefficients of a raising factorial polynomial sequence recursion: p(x, n) = (m*x + n - 1)*p(x, n - 1).
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1
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1, 0, 2, 0, 2, 4, 0, 4, 12, 8, 0, 12, 44, 48, 16, 0, 48, 200, 280, 160, 32, 0, 240, 1096, 1800, 1360, 480, 64, 0, 1440, 7056, 12992, 11760, 5600, 1344, 128, 0, 10080, 52272, 105056, 108304, 62720, 20608, 3584, 256, 0, 80640, 438336, 944992, 1076544, 718368
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are factorials.
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REFERENCES
| Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 62-63
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FORMULA
| p(x, n) = (m*x + n - 1)*p(x, n - 1).
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EXAMPLE
| {1},
{0, 2},
{0, 2, 4},
{0, 4, 12, 8},
{0, 12, 44, 48, 16},
{0, 48, 200, 280, 160, 32},
{0, 240, 1096, 1800, 1360, 480, 64},
{0, 1440, 7056, 12992, 11760,5600, 1344, 128},
{0, 10080, 52272, 105056, 108304, 62720, 20608, 3584, 256},
{0, 80640, 438336, 944992, 1076544, 718368, 290304, 69888, 9216, 512},
{0, 725760, 4106304, 9381600, 11578880, 8618400, 4049472, 1209600, 222720, 23040, 1024}
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MATHEMATICA
| m = 2; p[x, 0] = 1; p[x, -1] = 0; p[x, 1] = m*x; p[x_, n_] := p[x, n] = (m*x + n - 1)*p[x, n - 1]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]
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CROSSREFS
| Apart from signs, same as A137312.
Sequence in context: A194759 A126440 A131186 * A137312 A143507 A071961
Adjacent sequences: A137317 A137318 A137319 * A137321 A137322 A137323
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 20 2008
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