A370939 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-3*x)/3) ).

1, 1, 7, 93, 1848, 49194, 1646352, 66471138, 3145730760, 170825968008, 10472450056632, 715494753359352, 53913145327125840, 4441896708946850880, 397268517350608957440, 38332384702788360859344, 3969252425402471222357760, 439043217473917940361120000

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052802, A370938.

Cf. A370934, A370937.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-3*x)/3))/x))

PARI

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

Formula

a(n) = (1/(n+1)!) * Sum_{k=0..n} 3^(n-k) * (n+k)! * |Stirling1(n,k)|.