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

Author

Seiichi Manyama, Aug 17 2023

Keywords

• nonn

Crossrefs

Cf. A363357, A365034.

Cf. A364941.

Programs

PARI

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

Formula

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