A377545 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^3.

1, 3, 18, 195, 3108, 65595, 1730538, 54891165, 2036187576, 86536398195, 4147191867630, 221314773837333, 13017260705093604, 836754118106509083, 58364080427471191506, 4390560359156841730605, 354356981533262814367728, 30543768949098926368973667, 2800395449868306713606542422

Offset: 0

Author

Seiichi Manyama, Oct 31 2024

Keywords

• nonn

Crossrefs

Cf. A161633, A377541, A377551.

Cf. A364981.

Programs

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364981.

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