A229359 Total sum of n-th powers of parts in all partitions of 8.

86, 176, 558, 2486, 13578, 83486, 552378, 3835406, 27530298, 202345886, 1513288698, 11466138926, 87752274618, 676845479486, 5252962429818, 40970428516046, 320834049236538, 2520676708888286, 19857791921151738, 156791682937990766, 1240318818550256058

Offset: 0

Author

Alois P. Heinz, Sep 20 2013

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).

Crossrefs

Row n=8 of A213191.

Programs

Maple

a:= n-> 45+19*2^n+9*3^n+6*4^n+3*5^n+2*6^n+7^n+8^n:
seq(a(n), n=0..30);

Mathematica

LinearRecurrence[{36,-546,4536,-22449,67284,-118124,109584,-40320},{86,176,558,2486,13578,83486,552378,3835406},30] (* Harvey P. Dale, Aug 10 2021 *)

Formula

a(n) = Sum_{k=1..8} A066633(8,k) * k^n.

a(n) = 45 + 19*2^n + 9*3^n + 6*4^n + 3*5^n + 2*6^n + 7^n + 8^n.

G.f.: -2*(1213656*x^7 -2263598*x^6 +1707227*x^5 -680514*x^4 +155801*x^3 -20589*x^2 +1460*x -43) / Product_{j=1..8} (j*x-1).