A382643 Expansion of e.g.f. exp( x/(1-3*x)^(4/3) ).

1, 1, 9, 109, 1697, 32401, 733081, 19167709, 568351169, 18833921857, 689436160361, 27616959669421, 1201138514382049, 56349982190989969, 2835621797645900537, 152321976433436677981, 8697876904012444443521, 526015632425455532060929, 33581536744768011688139209

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} 3^(n-k) * binomial(n+k/3-1,n-k)/k!.

a(n) ~ 2^(3/7) * 3^(n + 1/14) * n^(n - 3/14) * exp(-2^(-2/7)*3^(-12/7)*n^(1/7) + 7*2^(-8/7)*3^(-6/7)*n^(4/7) - n) / sqrt(7). - Vaclav Kotesovec, Apr 17 2025

Prog

(PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*binomial(n+k/3-1, n-k)/k!);

Crossrefs

Cf. A362188, A362205, A382652.

Sequence in context: A349335 A291815 A261502 * A359731 A105974 A053912

Adjacent sequences: A382640 A382641 A382642 * A382644 A382645 A382646

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 03 2025

Status

approved