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Search: id:A156366
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| A156366 |
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Coefficients of infinite sum polynomials: p(x,n)=(1 - 3*x)^(n + 1)*Sum[3^k*(k + 1)^n*x^k, {k, 0, Infinity}]. |
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+0
1
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| 1, 1, 1, 3, 1, 12, 9, 1, 33, 99, 27, 1, 78, 594, 702, 81, 1, 171, 2718, 8154, 4617, 243, 1, 360, 10719, 65232, 96471, 29160, 729, 1, 741, 38637, 421713, 1265139, 1043199, 180063, 2187, 1, 1506, 131472, 2382318, 12651390, 21440862, 10649232, 1097874
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are:
{1, 1, 4, 22, 160, 1456, 15904, 202672, 2951680, 48361216, 880405504,...}.
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FORMULA
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p(x,n)=(1 - 3*x)^(n + 1)*Sum[3^k*(k + 1)^n*x^k, {k, 0, Infinity}];
p(x,n)=(1 - 3 x)^(1 + n)* PolyLog[ -n, 3 x]/(3*x);
t(n,m)=coefficients(p(x,n)).
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EXAMPLE
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{1},
{1},
{1, 3},
{1, 12, 9},
{1, 33, 99, 27},
{1, 78, 594, 702, 81},
{1, 171, 2718, 8154, 4617, 243},
{1, 360, 10719, 65232, 96471, 29160, 729},
{1, 741, 38637, 421713, 1265139, 1043199, 180063, 2187},
{1, 1506, 131472, 2382318, 12651390, 21440862, 10649232, 1097874, 6561},
{1, 3039, 430560, 12290184, 106138674, 318416022, 331834968, 104626080, 6646293, 19683}
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MATHEMATICA
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Clear[p, x, n, m];
p[x_, n_] = (1 - 3*x)^(n + 1)*Sum[3^k*(k + 1)^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
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Sequence in context: A049458 A143492 A062139 this_sequence A144353 A039811 A046089
Adjacent sequences: A156363 A156364 A156365 this_sequence A156367 A156368 A156369
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 08 2009
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