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A156653
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Coefficients of a higher level infinite sum polynomial: p(x,n)=(1 - x)^(2n + 1)/((n + 1)*x^n)*Sum[(k + 1)^n*Binomial[k, n]*x^ k, {k, 0, Infinity}].
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0
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1, 1, 3, 1, 16, 13, 1, 125, 171, 39, 1, 1296, 2551, 1091, 101, 1, 16807, 43653, 28838, 5498, 243, 1, 262144, 850809, 780585, 243790, 24270, 561, 1, 4782969, 18689527, 22278189, 10073955, 1733035, 98661, 1263, 1, 100000000, 457947691, 677785807
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Roe sums are:A001761;
{1, 1, 4, 30, 336, 5040, 95040, 2162160, 57657600, 1764322560, 60949324800,...}.
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FORMULA
| p(x,n)=(1 - x)^(2n + 1)/((n + 1)*x^n)*Sum[(k + 1)^n*Binomial[k, n]*x^ k, {k, 0, Infinity}];
t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {1},
{1},
{3, 1},
{16, 13, 1},
{125, 171, 39, 1},
{1296, 2551, 1091, 101, 1},
{16807, 43653, 28838, 5498, 243, 1},
{262144, 850809, 780585, 243790, 24270, 561, 1},
{4782969, 18689527, 22278189, 10073955, 1733035, 98661, 1263, 1},
{100000000, 457947691, 677785807, 410994583, 106215619, 10996369, 379693, 2797, 1},
{2357947691, 12400462713, 22055317500, 17027114412, 6066172434, 976428894, 64468572, 1406460, 6123, 1}
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MATHEMATICA
| Clear[p, x, n, m];
p[x_, n_] = (1 - x)^( 2n + 1)/((n + 1)*x^n)*Sum[(k + 1)^n*Binomial[k, n]*x^k, {k, 0, Infinity}];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A128249 A071211 A038675 * A048159 A123527 A096611
Adjacent sequences: A156650 A156651 A156652 * A156654 A156655 A156656
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 12 2009
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