A370941 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + 2*log(1-x)) ).

1, 2, 18, 304, 7668, 259048, 11001968, 563728464, 33857839360, 2333472749376, 181558569560448, 15743501573763456, 1505641080366272640, 157445985444107880960, 17872580693502293022720, 2188829492626563123881472, 287673783237906407512565760

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A258922, A370940.

Cf. A370938.

Programs

PARI

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

PARI

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

Formula

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