A377548 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x))^3 ).

1, 3, 36, 789, 25644, 1112655, 60584058, 3975599271, 305587795320, 26941234079259, 2680537845979470, 297158198268036963, 36325021999771692036, 4854553774172042934279, 704185171457954845825026, 110192472149320674192100815, 18503193203651913813111781488, 3318723221891108953801703239731

Offset: 0

Author

Seiichi Manyama, Oct 31 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A377546.

Cf. A365177.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x))^3)/x))

PARI

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

Formula

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A365177.

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