A355470 - OEIS

%I #12 Jul 03 2022 09:34:47

%S 1,1,66,21222,18927560,36030104000,125486684755152,722272396672485568,

%T 6391048590559497227904,82362961035803105954736768,

%U 1482370265813455598541301007360,36031982428595760278113744699088384,1150873035676373345725887922070318410752

%N Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1).

%F E.g.f.: Sum_{k>=0} exp(k^3 * x) * (k^3 * x)^k/k!.

%F a(n) = Sum_{k=0..n} k^(3*n) * binomial(n,k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*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)*(k^3*x)^k/k!)))

%o (PARI) a(n) = sum(k=0, n, k^(3*n)*binomial(n, k));

%Y Cf. A355469, A355473.

%Y Cf. A072034, A242446, A355466.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 03 2022