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

0,3

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

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

Prog

(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)!;

Crossrefs

Cf. A052802, A370939.

Sequence in context: A256238 A388537 A359714 * A349557 A140606 A355219

Adjacent sequences: A370935 A370936 A370937 * A370939 A370940 A370941

Keyword

nonn

Author

Seiichi Manyama, Mar 06 2024

Status

approved