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

Author

Seiichi Manyama, Feb 02 2025

Keywords

• nonn

Crossrefs

Cf. A380765.

Programs

PARI

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

Formula

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