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A355470 Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1). 3
1, 1, 66, 21222, 18927560, 36030104000, 125486684755152, 722272396672485568, 6391048590559497227904, 82362961035803105954736768, 1482370265813455598541301007360, 36031982428595760278113744699088384, 1150873035676373345725887922070318410752 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Sum_{k>=0} exp(k^3 * x) * (k^3 * x)^k/k!.
a(n) = Sum_{k=0..n} k^(3*n) * binomial(n,k).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1-k^3*x)^(k+1)))
(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!)))
(PARI) a(n) = sum(k=0, n, k^(3*n)*binomial(n, k));
CROSSREFS
Sequence in context: A282247 A197439 A127706 * A356688 A167778 A199838
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 03 2022
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)