A376441 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2))^2 ).

1, 0, 0, 12, 0, 120, 10800, 3360, 766080, 56064960, 76507200, 12988926720, 885913459200, 3162288729600, 477701680135680, 31728803730624000, 230820218044416000, 32828647402065715200, 2173902177236319129600, 27658882036996206796800, 3801535675181689116672000, 255228267875636473786368000

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Index entries for reversions of series

Formula

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

a(n) = (2 * n!/(2n+2)!) * Sum_{k=0..floor(n/2)} (3*n-2*k+1)! * |Stirling1(k,n-2*k)|/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2))^2)/x))
(PARI) a(n) = 2*n!*sum(k=0, n\2, (3*n-2*k+1)!*abs(stirling(k, n-2*k, 1))/k!)/(2*n+2)!;

Crossrefs

Cf. A376344, A376442.

Cf. A375680.

Sequence in context: A375664 A375680 A376443 * A077351 A370018 A119530

Adjacent sequences: A376438 A376439 A376440 * A376442 A376443 A376444

Keyword

nonn

Author

Seiichi Manyama, Sep 22 2024

Status

approved