A380722 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 * (1 - x*A(x))) / (1 - x*A(x))^2.

1, 3, 33, 679, 20905, 863601, 44912347, 2820755183, 207815625073, 17578781394913, 1679410405425571, 178871724214036767, 21017369600310686665, 2700840226820242034321, 376826763817725194699083, 56730569139675562422229711, 9166624006966363722766482913, 1582356756863532248954506939329

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, A380721.

Sequence in context: A376393 A380666 A379860 * A091462 A340971 A326328

Adjacent sequences: A380719 A380720 A380721 * A380723 A380724 A380726

Keyword

nonn,new

Author

Seiichi Manyama, Jan 30 2025

Status

approved