A380771 E.g.f. A(x) satisfies A(x) = exp(x * A(x) * (1 + x*A(x)^2)) * (1 + x*A(x)^2).

1, 2, 17, 277, 6797, 224301, 9327235, 468615379, 27624235385, 1869871826521, 142960839681311, 12185757382882623, 1145898471300898837, 117849030630765668677, 13159165724143312996907, 1585485015346749680509051, 205026978076680944633853425, 28324382622872897021731667121

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

(PARI) a(n, q=1, r=2, s=1, 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!);

Crossrefs

Cf. A380768.

Sequence in context: A379691 A338635 A268705 * A380718 A078367 A377888

Adjacent sequences: A380765 A380768 A380769 * A380772 A380773 A380774

Keyword

nonn,new

Author

Seiichi Manyama, Feb 02 2025

Status

approved