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%I #6 Aug 10 2021 13:25:39
%S 86,176,558,2486,13578,83486,552378,3835406,27530298,202345886,
%T 1513288698,11466138926,87752274618,676845479486,5252962429818,
%U 40970428516046,320834049236538,2520676708888286,19857791921151738,156791682937990766,1240318818550256058
%N Total sum of n-th powers of parts in all partitions of 8.
%H Alois P. Heinz, <a href="/A229359/b229359.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).
%F a(n) = Sum_{k=1..8} A066633(8,k) * k^n.
%F a(n) = 45 + 19*2^n + 9*3^n + 6*4^n + 3*5^n + 2*6^n + 7^n + 8^n.
%F 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).
%p a:= n-> 45+19*2^n+9*3^n+6*4^n+3*5^n+2*6^n+7^n+8^n:
%p seq(a(n), n=0..30);
%t LinearRecurrence[{36,-546,4536,-22449,67284,-118124,109584,-40320},{86,176,558,2486,13578,83486,552378,3835406},30] (* _Harvey P. Dale_, Aug 10 2021 *)
%Y Row n=8 of A213191.
%K nonn,easy
%O 0,1
%A _Alois P. Heinz_, Sep 20 2013
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