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Search: id:A137312
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| A137312 |
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A triangular sequence from a coefficients of generalized factorial polynomial recursion from Roman:a=1/2; p(x, n) = (x/a - (n - 1))*p(x, n - 1). |
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+0
2
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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, -290304, 69888, -9216, 512, 0
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0}
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REFERENCES
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Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 56-57
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FORMULA
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p(x,0)=1;p(x,1)=x/a;a=1/2; p(x, n) = (x/a - (n - 1))*p(x, n - 1).
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EXAMPLE
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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, -290304, 69888, -9216, 512},
{0, -725760, 4106304, -9381600,11578880, -8618400, 4049472, -1209600, 222720, -23040, 1024}
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MATHEMATICA
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a = 1/2; p[x, 0] = 1; p[x, 1] = x/a; p[x_, n_] := p[x, n] = (x/a - (n - 1))*p[x, n - 1]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a0]
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CROSSREFS
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Apart from signs, same as A137320.
Sequence in context: A126440 A131186 A137320 this_sequence A143507 A071961 A120557
Adjacent sequences: A137309 A137310 A137311 this_sequence A137313 A137314 A137315
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 20 2008
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