A355473 Expansion of Sum_{k>=0} x^k/(1 - k^3 * x)^(k+1).

1, 1, 3, 28, 497, 12736, 517297, 28793248, 2095968065, 199522773568, 23839495688321, 3482169003693304, 616298415199306369, 130134007837039167040, 32272959284595295173377, 9313050358489324003967176, 3101245112865402456422252033

Offset

0,3

Links

Winston de Greef, Table of n, a(n) for n = 0..235

Formula

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

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, 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)*x^k/k!)))
(PARI) a(n) = sum(k=0, n, k^(3*(n-k))*binomial(n, k));

Crossrefs

Cf. A000248, A135746, A355464.

Sequence in context: A058804 A327114 A327336 * A180710 A005328 A192559

Adjacent sequences: A355470 A355471 A355472 * A355474 A355475 A355476

Keyword

nonn

Author

Seiichi Manyama, Jul 03 2022

Status

approved