A376437 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2*log(1-x))^3 ).

1, 0, 0, 18, 36, 120, 24300, 192024, 1572480, 194205600, 3380922720, 50671716480, 4879442177280, 144175221440640, 3391736273557632, 287077095515548800, 12328722259931750400, 413067654425986560000, 33216197499043235527680

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 * log(1 - x*A(x)))^3.

a(n) = (3 * n!/(3*n+3)!) * Sum_{k=0..floor(n/3)} (3*n+k+2)! * |Stirling1(n-2*k,k)|/(n-2*k)!.

Prog

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

Crossrefs

Cf. A376386, A376393.

Cf. A375679.

Sequence in context: A335784 A347889 A375679 * A115550 A061713 A198802

Adjacent sequences: A376434 A376435 A376436 * A376438 A376439 A376440

Keyword

nonn

Author

Seiichi Manyama, Sep 22 2024

Status

approved