A380774 E.g.f. A(x) satisfies A(x) = exp(x / (1 + x*A(x))^2) * (1 + x*A(x))^2.

1, 3, 15, 121, 1493, 25041, 519175, 12764109, 365437385, 11989334305, 443413796291, 18237280179669, 825743182996957, 40830652259369649, 2189754246873652607, 126605689000719768541, 7850410500340268709137, 519697910250629229492033, 36585510030973732956134779

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} (n-k+1)^(k-1) * binomial(2*n-4*k+2,n-k)/k!.

Prog

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

Crossrefs

Cf. A380765.

Sequence in context: A377105 A160884 A173468 * A197505 A348903 A191371

Adjacent sequences: A380771 A380772 A380773 *

Keyword

nonn,new

Author

Seiichi Manyama, Feb 02 2025

Status

approved