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A229359 Total sum of n-th powers of parts in all partitions of 8. 2
86, 176, 558, 2486, 13578, 83486, 552378, 3835406, 27530298, 202345886, 1513288698, 11466138926, 87752274618, 676845479486, 5252962429818, 40970428516046, 320834049236538, 2520676708888286, 19857791921151738, 156791682937990766, 1240318818550256058 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 10:47 EST 2022. Contains 350454 sequences. (Running on oeis4.)