A370938 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-2*x)/2) ).

1, 1, 6, 68, 1152, 26144, 745952, 25678512, 1036151680, 47977039488, 2507929819392, 146106188393472, 9387670177320960, 659534185673994240, 50299364999073742848, 4138631751212820025344, 365438936930414973419520, 34469156894239754317332480

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052802, A370939.

Programs

PARI

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

PARI

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

Formula

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