A376442 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2))^3 ).

1, 0, 0, 18, 0, 180, 23760, 5040, 1693440, 180260640, 169646400, 42116215680, 4148153856000, 10311946444800, 2266331900152320, 215416210961952000, 1103951255139532800, 227420391096138240000, 21290356810886504140800, 193675502529294757171200, 38377888101603670523904000

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A376344, A376441.

Cf. A375681.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2))^3)/x))

PARI

a(n) = 3*n!*sum(k=0, n\2, (4*n-2*k+2)!*abs(stirling(k, n-2*k, 1))/k!)/(3*n+3)!;

Formula

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

a(n) = (3 * n!/(3n+3)!) * Sum_{k=0..floor(n/2)} (4*n-2*k+2)! * |Stirling1(k,n-2*k)|/k!.