A376439 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*(exp(x) - 1))^3 ).

1, 0, 0, 18, 36, 60, 23850, 189126, 988008, 184207176, 3254640750, 35132272890, 4418970811596, 134653558474188, 2463781708180338, 246532610826062190, 11098269938629561680, 305828547775319369616, 27016544700449293891158

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = 1/(1 - x^2*A(x)^2 * (exp(x*A(x)) - 1))^3.

a(n) = (3 * n!/(3*n+3)!) * Sum_{k=0..floor(n/3)} (3*n+k+2)! * Stirling2(n-2*k,k)/(n-2*k)!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*(exp(x)-1))^3)/x))
(PARI) a(n) = 3*n!*sum(k=0, n\3, (3*n+k+2)!*stirling(n-2*k, k, 2)/(n-2*k)!)/(3*n+3)!;

Crossrefs

Cf. A376382, A376390.

Cf. A375663.

Sequence in context: A154575 A344199 A375663 * A097926 A087967 A070224

Adjacent sequences: A376436 A376437 A376438 * A376440 A376441 A376442

Keyword

nonn

Author

Seiichi Manyama, Sep 22 2024

Status

approved