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A368527 a(n) = Sum_{k=1..n} k^3 * n^k.

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%I A368527 #11 Dec 29 2023 08:05:37
%S A368527 0,1,34,804,18244,434205,11138766,310151632,9370253320,306232628625,
%T A368527 10783859167810,407523041660196,16461877678462668,708207095198943613,
%U A368527 32338800248010936694,1562509380160144645440,79657105206246202521616
%N A368527 a(n) = Sum_{k=1..n} k^3 * n^k.
%F A368527 a(n) = [x^n] n*x * (1+4*n*x+(n*x)^2)/((1-x) * (1-n*x)^4).
%F A368527 a(n) = n * (n^n * (n^6-3*n^5+8*n^3-4*n^2-7*n-1) + n^2 + 4*n + 1)/(n-1)^4 for n > 1.
%o A368527 (PARI) a(n) = sum(k=1, n, k^3*n^k);
%Y A368527 Cf. A062806, A303991, A368526.
%Y A368527 Cf. A368525.
%K A368527 nonn,easy
%O A368527 0,3
%A A368527 _Seiichi Manyama_, Dec 28 2023