A381988 E.g.f. A(x) satisfies A(x) = exp(x) * B(x*A(x)), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.

1, 2, 15, 313, 10773, 510981, 30876463, 2267990159, 196204786025, 19539828320905, 2201822913234771, 276969947671828995, 38473403439454795837, 5849221857618942870029, 966078641687956464576119, 172251173569831561500070711, 32975613823747758363130520529, 6746227557293225645352382744593

Offset: 0

Author

Seiichi Manyama, Mar 12 2025

Keywords

• nonn

Crossrefs

Cf. A381987, A381989.

Cf. A002293, A002294, A346647, A377526.

Programs

PARI

a(n) = n!*sum(k=0, n, (k+1)^(n-k)*binomial(5*k+1, k)/((5*k+1)*(n-k)!));

Formula

Let F(x) be the e.g.f. of A377526. F(x) = B(x*A(x)) = exp( 1/4 * Sum_{k>=1} binomial(4*k,k) * (x*A(x))^k/k ).

a(n) = n! * Sum_{k=0..n} (k+1)^(n-k) * A002294(k)/(n-k)!.