A377503 E.g.f. satisfies A(x) = 1/(1 - x * exp(x) * A(x))^2.

1, 2, 18, 270, 5936, 173330, 6335772, 278724362, 14350790064, 847007698338, 56397332340020, 4182866692785242, 342022887565717800, 30570009715185100082, 2965368922693150575084, 310276298423966343555690, 34834957115496822249510752, 4177193847524372747798263106

Offset: 0

Author

Seiichi Manyama, Oct 30 2024

Keywords

• nonn

Crossrefs

Cf. A295238, A377504, A377528.

Cf. A006013, A364983.

Programs

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364983.

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