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A176863
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A triangle sequence from coefficients of an infinite sum polynomial: p(x,n)=Sum[(n - k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n)
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0
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1, 0, -1, 4, -3, 1, 64, -36, 9, -1, 1296, -650, 147, -18, 1, 32768, -15440, 3330, -415, 30, -1, 1000000, -452984, 95070, -11915, 945, -45, 1, 35831808, -15796032, 3257240, -409290, 33985, -1869, 63, -1, 1475789056, -637771728, 129899980
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OFFSET
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0,4
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COMMENTS
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Row sums are:
{1, -1, 2, 36, 776, 20272, 631072, 22915904, 952885376, 44690261760,
2334989427200,...}.
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LINKS
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FORMULA
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p(x,n)=Sum[(n - k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n);
t(n,m)=coefficients(p(x,n))
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EXAMPLE
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{1},
{0, -1},
{4, -3, 1},
{64, -36, 9, -1},
{1296, -650, 147, -18, 1},
{32768, -15440, 3330, -415, 30, -1},
{1000000, -452984, 95070, -11915, 945, -45, 1},
{35831808, -15796032, 3257240, -409290, 33985, -1869, 63, -1},
{1475789056, -637771728, 129899980, -16347156, 1394785, -82824, 3346, -84, 1},
{68719476736, -29249804544, 5903488080, -743652588, 64602132, -4022361, 179760, -5562, 108, -1},
{3570467226624, -1501631050304, 300957690720, -37937816820, 3338126820, -214628631, 10227105, -356910, 8730, -135, 1}
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MATHEMATICA
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p[x_, n_] := Sum[(n - k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n);
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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