A380773 E.g.f. A(x) satisfies A(x) = exp(x / (1 + x*A(x))) * (1 + x*A(x))^2.

1, 3, 17, 157, 2081, 36301, 787435, 20454393, 619606321, 21459697561, 836857705931, 36298027042069, 1733720198941945, 90434688020581893, 5115766921884661099, 311966602078171218481, 20402441541405767271137, 1424538121070974347467569, 105769440064498860592940683

Offset: 0

Author

Seiichi Manyama, Feb 02 2025

Keywords

• nonn

Crossrefs

Cf. A380764.

Programs

PARI

a(n, q=1, r=1, s=0, t=-1, 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-3*k+2,n-k)/k!.