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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
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; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are:

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

LINKS

Table of n, a(n) for n=0..44.

FORMULA

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)).

EXAMPLE

{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}

MATHEMATICA

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[%]

CROSSREFS

Sequence in context: A143492 A243662 A062139 * A144353 A039811 A046089

Adjacent sequences:  A156363 A156364 A156365 * A156367 A156368 A156369

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 08 2009

STATUS

approved

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Last modified March 24 19:41 EDT 2019. Contains 321448 sequences. (Running on oeis4.)