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

0,1

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).

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).

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 *)

Crossrefs

Row n=8 of A213191.

Sequence in context: A098466 A044256 A044637 * A063353 A044418 A044799

Adjacent sequences: A229356 A229357 A229358 * A229360 A229361 A229362

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 20 2013

Status

approved