A372201 E.g.f. A(x) satisfies A(x) = exp( 3 * x / (1 - x * A(x)^(1/3))^3 ).

1, 3, 27, 351, 6309, 145143, 4083669, 136159299, 5256248265, 230783968395, 11364265672929, 620524946670687, 37222254648712989, 2433741005377774719, 172301622840992025117, 13133140607475128862747, 1072406955985984437773841, 93406430850089038192704915

Offset

0,2

Links

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

Formula

E.g.f.: A(x) = B(x)^3 where B(x) is the e.g.f. of A364938.

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!.

Prog

(PARI) a(n, r=3, s=3, 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!);

Crossrefs

Cf. A161630, A372200.

Cf. A364938.

Sequence in context: A168593 A364431 A328182 * A370288 A157089 A365794

Adjacent sequences: A372198 A372199 A372200 * A372202 A372203 A372204

Keyword

nonn

Author

Seiichi Manyama, Apr 21 2024

Status

approved