A380753 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x * A(x)^2)^2.

1, 3, 47, 1453, 68349, 4344751, 348936139, 33912469305, 3871084443641, 507765120717691, 75265926888996711, 12443096536067016997, 2270083842550815380725, 453042725968243823206887, 98183026886745981671902979, 22962952582930039784948279281, 5764815614414943166224203759601

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(5*n-k+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (2*n+1)^(k-1)*binomial(5*n-k+1, n-k)/k!);

Crossrefs

Cf. A377745, A380752.

Cf. A380723.

Sequence in context: A383121 A385528 A187665 * A088718 A355256 A354556

Adjacent sequences: A380750 A380751 A380752 * A380754 A380755 A380756

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2025

Status

approved