A380721 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x))^3) / (1 - x*A(x))^2.

1, 3, 29, 511, 13313, 462401, 20140495, 1056765711, 64931273601, 4575023966017, 363744086548751, 32219262817769039, 3146690718151835233, 335963164545043929921, 38931639595489583488239, 4866587415704561667715471, 652773358729046023136421377, 93523037570967777721191018881

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

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

Crossrefs

Cf. A380665, A380722.

Sequence in context: A113871 A379862 A377832 * A380781 A186451 A248828

Adjacent sequences: A380718 A380719 A380720 * A380722 A380723 A380724

Keyword

nonn,new

Author

Seiichi Manyama, Jan 30 2025

Status

approved