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A154646 Triangle T(n,k) with the coefficient [x^k] of the series (1-x)^(n+1)* sum_{m=0..infinity} [(3*m+1)^n + (3*m+2)^n]*x^m in row n, column k. 2
2, 3, 3, 5, 26, 5, 9, 153, 153, 9, 17, 796, 2262, 796, 17, 33, 3951, 25176, 25176, 3951, 33, 65, 19266, 243111, 524876, 243111, 19266, 65, 129, 93477, 2168235, 8760639, 8760639, 2168235, 93477, 129, 257, 453848, 18445820, 127880936, 235517318 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are 2, 6, 36, 324, 3888, 58320, 1049760, 22044960, 529079040, 14285134080,

428554022400,...

LINKS

Table of n, a(n) for n=0..40.

EXAMPLE

2;

3, 3;

5, 26, 5;

9, 153, 153, 9;

17, 796, 2262, 796, 17;

33, 3951, 25176, 25176, 3951, 33;

65, 19266, 243111, 524876, 243111, 19266, 65;

129, 93477, 2168235, 8760639, 8760639, 2168235, 93477, 129;

257, 453848, 18445820, 127880936, 235517318, 127880936, 18445820, 453848, 257;

MAPLE

A154646 := proc(n, k)

    (-1)^(n+1)*(x-1)^(n+1)*add(x^j*((3*j+1)^n+(3*j+2)^n), j=0..k) ;

    coeftayl(%, x=0, k) ;

end proc: # R. J. Mathar, Jul 23 2012

MATHEMATICA

Clear[p]; p[x_, n_] = (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(3*m + 2)^n*x^m, {m, 0, Infinity}]

+ (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(3*m + 1)^n*x^m, {m, 0, Infinity}];

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

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

Flatten[%]

Contribution from Roger L. Bagula, Nov 27 2009: (Start)

p[t_] = Exp[t]*x/((-Exp[3*t] + x)) + Exp[2*t]*x/((-Exp[3*t] + x));

a = Table[ CoefficientList[FullSimplify[ExpandAll[(n!*(-1 + x)^(n + 1)/x)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}];

Flatten[a] (End)

CROSSREFS

Sequence in context: A270592 A096659 A154695 * A046826 A323713 A054892

Adjacent sequences:  A154643 A154644 A154645 * A154647 A154648 A154649

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Jan 13 2009

STATUS

approved

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Last modified August 11 18:37 EDT 2020. Contains 336428 sequences. (Running on oeis4.)