A376392 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^2 ).

1, 2, 16, 238, 5270, 156048, 5803980, 260301564, 13679476864, 824735208864, 56125075306656, 4256136846770400, 355933078611032880, 32544591173495688480, 3230049230183020829184, 345849932418702558032736, 39738632934736396340588160, 4877326190739889592547393792

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052801, A367138.

Programs

PARI

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

PARI

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

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367138.

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