A380726 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 / (1 - x*A(x)^2)) / (1 - x*A(x)^2).

1, 2, 23, 526, 18345, 865426, 51606511, 3725086590, 315869177777, 30781410753250, 3390102419068071, 416446509483046318, 56455962861401232025, 8372599773137199223794, 1348414830158700569758655, 234364024637335981658563486, 43725325359127416298442233569

Offset: 0

Author

Seiichi Manyama, Jan 31 2025

Keywords

• nonn

Crossrefs

Cf. A380663, A380727.

Cf. A380723.

Programs

PARI

a(n) = n!*sum(k=0, n, (2*n+1)^(k-1)*binomial(3*n, n-k)/k!);

Formula

a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(3*n,n-k)/k!.