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%I #14 Apr 12 2022 11:12:56
%S 1,1,63,19172,16249870,29458152441,97813591721181,537081363012854224,
%T 4535464309375188976956,55796581668379082029481225,
%U 958824462567528346234944706075,22255431432328421226838750870120356,678866987929798923743810982299237129610
%N a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n).
%F G.f.: Sum_{k>=0} (k^3 * x)^k/(1 + k^3 * x).
%F a(n) ~ 1/(1 + exp(-3)) * n^(3*n). - _Vaclav Kotesovec_, Dec 10 2021
%t Join[{1},Table[Sum[(-1)^(n-k) k^(3n),{k,0,n}],{n,20}]] (* _Harvey P. Dale_, Apr 12 2022 *)
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*k^(3*n));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1+k^3*x)))
%Y Cf. A120485, A349885, A349889, A349891.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 05 2021
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