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%I #16 Aug 24 2022 12:09:20
%S 1,1,66,21225,18952156,36175231585,126556309395486,733064060959310689,
%T 6540867625730306094360,85180334386943946887707617,
%U 1552697061493449955344530003290,38315904135534199560725372265381721,1245605749857294018587318829355458646068
%N a(n) = n! * Sum_{k=0..n} k^(3*n)/k!.
%H Seiichi Manyama, <a href="/A356688/b356688.txt">Table of n, a(n) for n = 0..149</a>
%F E.g.f.: Sum_{k>=0} (k^3 * x)^k / (k! * (1 - k^3 * x)).
%t a[n_] := n! * Sum[k^(3*n)/k!, {k, 0, n}]; a[0] = 1; Array[a, 13, 0] (* _Amiram Eldar_, Aug 23 2022 *)
%o (PARI) a(n) = n!*sum(k=0, n, k^(3*n)/k!);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*x)^k/(k!*(1-k^3*x)))))
%Y Cf. A256016, A356687.
%Y Cf. A337001, A349901, A356673.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 23 2022
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