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A156366 Coefficients of infinite sum polynomials: p(x,n)=(1 - 3*x)^(n + 1)*Sum[3^k*(k + 1)^n*x^k, {k, 0, Infinity}]. 0

%I

%S 1,1,1,3,1,12,9,1,33,99,27,1,78,594,702,81,1,171,2718,8154,4617,243,1,

%T 360,10719,65232,96471,29160,729,1,741,38637,421713,1265139,1043199,

%U 180063,2187,1,1506,131472,2382318,12651390,21440862,10649232,1097874

%N Coefficients of infinite sum polynomials: p(x,n)=(1 - 3*x)^(n + 1)*Sum[3^k*(k + 1)^n*x^k, {k, 0, Infinity}].

%C Row sums are:

%C {1, 1, 4, 22, 160, 1456, 15904, 202672, 2951680, 48361216, 880405504,...}.

%F p(x,n)=(1 - 3*x)^(n + 1)*Sum[3^k*(k + 1)^n*x^k, {k, 0, Infinity}];

%F p(x,n)=(1 - 3 x)^(1 + n)* PolyLog[ -n, 3 x]/(3*x);

%F t(n,m)=coefficients(p(x,n)).

%e {1},

%e {1},

%e {1, 3},

%e {1, 12, 9},

%e {1, 33, 99, 27},

%e {1, 78, 594, 702, 81},

%e {1, 171, 2718, 8154, 4617, 243},

%e {1, 360, 10719, 65232, 96471, 29160, 729},

%e {1, 741, 38637, 421713, 1265139, 1043199, 180063, 2187},

%e {1, 1506, 131472, 2382318, 12651390, 21440862, 10649232, 1097874, 6561},

%e {1, 3039, 430560, 12290184, 106138674, 318416022, 331834968, 104626080, 6646293, 19683}

%t Clear[p, x, n, m];

%t p[x_, n_] = (1 - 3*x)^(n + 1)*Sum[3^k*(k + 1)^n*x^k, {k, 0, Infinity}];

%t Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];

%t Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl,uned

%O 0,4

%A _Roger L. Bagula_, Feb 08 2009

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Last modified October 28 18:25 EDT 2020. Contains 338064 sequences. (Running on oeis4.)