A355466 -id:A355466 - cp's OEIS frontend

A355470 Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1).

1, 1, 66, 21222, 18927560, 36030104000, 125486684755152, 722272396672485568, 6391048590559497227904, 82362961035803105954736768, 1482370265813455598541301007360, 36031982428595760278113744699088384, 1150873035676373345725887922070318410752

Offset: 0

Seiichi Manyama, Jul 03 2022

nonn

Cf. A355469, A355473.

Cf. A072034, A242446, A355466.

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1-k^3*x)^(k+1)))

my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp(k^3*x)*(k^3*x)^k/k!)))

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

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).

A355465 Expansion of Sum_{k>=0} (k^k * x/(1 - k^k * x))^k.

Original entry on oeis.org

1, 1, 17, 19812, 4296562388, 298027622009561768, 10314429455106223377205859112, 256923580408437742134605162130019436138968, 6277101736867794060924264576844540796924098543875220742528

Offset: 0

Seiichi Manyama, Jul 03 2022

nonn

Cf. A349886, A355466.

my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, (k^k*x/(1-k^k*x))^k))

a(n) = if(n==0, 1, sum(k=1, n, k^(k*n)*binomial(n-1, k-1)));

a(n) = Sum_{k=1..n} k^(k*n) * binomial(n-1,k-1) for n > 0.

cp's OEIS Frontend

A355470 Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1).

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A355465 Expansion of Sum_{k>=0} (k^k * x/(1 - k^k * x))^k.

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula