A365033 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))^2).

1, 1, 9, 127, 2769, 80861, 2976733, 132394011, 6909143265, 414041227417, 28025981914581, 2115049310887679, 176095675272002929, 16035108243371426613, 1585349332849711046829, 169128107565128349122851, 19365426435579375683158977, 2368882573995841615546652081

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A363357, A365034.

Cf. A364941.

Sequence in context: A366036 A258294 A362776 * A073014 A046754 A203425

Adjacent sequences: A365030 A365031 A365032 * A365034 A365035 A365036

Keyword

nonn

Author

Seiichi Manyama, Aug 17 2023

Status

approved