A376385 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x))^2 ).

1, 0, 4, 6, 280, 1620, 67788, 844200, 36344992, 752867136, 34869857040, 1039132179360, 52776841318848, 2066262237673920, 115959403155851136, 5617102749187849920, 348802585405252070400, 20063354348482794961920, 1375625132090917881338880

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370993, A376386.

Cf. A371230, A375671.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x))^2)/x))

PARI

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

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371230.

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