A377737 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - log(1-2*x) / 2) ).

1, 1, 4, 32, 392, 6504, 136464, 3466224, 103425664, 3546396288, 137423600640, 5939224680960, 283254408582144, 14777481937449984, 837175325044101120, 51182161648716349440, 3358765321328869539840, 235492308312669671424000, 17568539556367396687183872

Offset: 0

Author

Seiichi Manyama, Nov 08 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A138013, A377803.

Cf. A201595, A227917, A370938, A377789.

Programs

PARI

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

PARI

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

Formula

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