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%I #15 Feb 21 2023 23:25:30
%S 1,1,3,28,497,12736,517297,28793248,2095968065,199522773568,
%T 23839495688321,3482169003693304,616298415199306369,
%U 130134007837039167040,32272959284595295173377,9313050358489324003967176,3101245112865402456422252033
%N Expansion of Sum_{k>=0} x^k/(1 - k^3 * x)^(k+1).
%H Winston de Greef, <a href="/A355473/b355473.txt">Table of n, a(n) for n = 0..235</a>
%F E.g.f.: Sum_{k>=0} exp(k^3 * x) * x^k/k!.
%F a(n) = Sum_{k=0..n} k^(3*(n-k)) * binomial(n,k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^3*x)^(k+1)))
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp(k^3*x)*x^k/k!)))
%o (PARI) a(n) = sum(k=0, n, k^(3*(n-k))*binomial(n, k));
%Y Cf. A000248, A135746, A355464.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jul 03 2022
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