A372161 E.g.f. A(x) satisfies A(x) = exp( 3 * x / (1 - x * A(x)^(1/3)) ).

1, 3, 15, 117, 1269, 17763, 305829, 6264261, 148974009, 4037901219, 122940227169, 4155745911837, 154473245377317, 6263647154467875, 275184369838089357, 13023134386197318837, 660560328648108969201, 35751895401064184128707

Offset: 0

Author

Seiichi Manyama, Apr 20 2024

Keywords

• nonn

Crossrefs

Cf. A161630.

Programs

PARI

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

Formula

E.g.f.: A(x) = B(x)^3 where B(x) is the e.g.f. of A161630.

If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.