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

0,2

Links

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

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)! ).

Prog

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

Crossrefs

Cf. A295238, A377504, A377528.

Cf. A006013, A364983.

Sequence in context: A292693 A351275 A364400 * A334242 A349314 A365555

Adjacent sequences: A377500 A377501 A377502 * A377504 A377505 A377506

Keyword

nonn

Author

Seiichi Manyama, Oct 30 2024

Status

approved