A380765 E.g.f. A(x) satisfies A(x) = exp(x * (1 - x*A(x))^2) / (1 - x*A(x))^2.

1, 3, 19, 241, 4853, 131601, 4466875, 182546421, 8739580841, 480023587297, 29759608788551, 2055884656223949, 156623317577663293, 13045653418406432721, 1179479817324874518419, 115042876530398843323621, 12041278143223263581774417, 1346252625757920938545507521

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..n} (n-k+1)^(k-1) * binomial(3*n-5*k+1,n-k)/k!.

Prog

(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+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);

Crossrefs

Cf. A377742, A380764.

Sequence in context: A355216 A135754 A340225 * A118023 A054590 A261495

Adjacent sequences: A380762 A380763 A380764 * A380768 A380769 A380771

Keyword

nonn,new

Author

Seiichi Manyama, Feb 01 2025

Status

approved