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A156654
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Coefficients of a higher level infinite sum polynomial: p(x,n)=(1 - x)^(2n + 1)/(x^n)*Sum[(2*k + 1)^n*Binomial[k, n]*x^k, {k, 0, Infinity}].
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0
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1, 3, 1, 25, 22, 1, 343, 515, 101, 1, 6561, 14156, 5766, 396, 1, 161051, 456197, 299342, 49642, 1447, 1, 4826809, 16985858, 15796159, 4592764, 371239, 5090, 1, 170859375, 719818759, 878976219, 383355555, 58474285, 2550165, 17481, 1, 6975757441
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Roe sums are:A052714;
{1, 4, 48, 960, 26880, 967680, 42577920, 2214051840, 132843110400,
9033331507200, 686533194547200
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FORMULA
| p(x,n)=(1 - x)^(2n + 1)/(x^n)*Sum[(2*k + 1)^n*Binomial[k, n]*x^k, {k, 0, Infinity}];
t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {1},
{3, 1},
{25, 22, 1},
{343, 515, 101, 1},
{6561, 14156, 5766, 396, 1},
{161051, 456197, 299342, 49642, 1447, 1},
{4826809, 16985858, 15796159, 4592764, 371239, 5090, 1},
{170859375, 719818759, 878976219, 383355555, 58474285, 2550165, 17481, 1},
{6975757441, 34264190872, 52246537948, 31191262504, 7488334150, 660394024, 16574428, 59032, 1},
{322687697779, 1811734208009, 3329783850284, 2563367714324, 872277734234, 126505988606, 6870434876, 103682276, 196811, 1},
{16679880978201, 105414122807918, 227501403350541, 216602727685224, 97632310949922, 20706515546388, 1928212521522, 67389166824, 630891141, 649518, 1}
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MATHEMATICA
| Clear[p, x, n, m];
p[x_, n_] = (1 - x)^(2n + 1)/(x^n)*Sum[(2*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: A072271 A193472 A104033 * A098815 A033464 A170924
Adjacent sequences: A156651 A156652 A156653 * A156655 A156656 A156657
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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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