A380772 E.g.f. A(x) satisfies A(x) = exp(x * (1 + x*A(x)^2)) * (1 + x*A(x)^2).

1, 2, 13, 166, 3157, 80466, 2578969, 99734230, 4521335081, 235215564706, 13815024321061, 904313739020550, 65287579679979133, 5153929267246018546, 441668985219603417137, 40834603462763102240566, 4051601326622081640558673, 429423186979619018132841282

Offset: 0

Author

Seiichi Manyama, Feb 02 2025

Keywords

• nonn

Crossrefs

Cf. A380769.

Programs

PARI

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