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A355493
Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - x)^(k+1).
2
1, 2, 67, 19879, 16856337, 30601661681, 101743314190033, 559257425236996361, 4726837695171258085569, 58192258417571877186113281, 1000581709943568968705788233921, 23236157618902718144948494353385025, 709080642850925779233576351761544968833
OFFSET
0,2
LINKS
FORMULA
E.g.f.: exp(x) * Sum_{k>=0} (k^3 * x)^k/k!.
a(n) = Sum_{k=0..n} k^(3*k) * binomial(n,k).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1-x)^(k+1)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, (k^3*x)^k/k!)))
(PARI) a(n) = sum(k=0, n, k^(3*k)*binomial(n, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 04 2022
STATUS
approved