A328007 Expansion of e.g.f. 1 / (2 - exp(-x) / (1 - x)).

1, 0, 1, 2, 15, 84, 705, 6222, 65779, 765608, 9999333, 143009250, 2235857943, 37833382716, 689729792713, 13469761663862, 280613761282875, 6211105772020560, 145566258957724845, 3601055676894146442, 93772841089130278495, 2563969299245947753700, 73443322391840827563921

Offset: 0

Author

Ilya Gutkovskiy, Oct 01 2019

Keywords

• nonn

Crossrefs

Cf. A000166, A002866, A302557, A321989, A328008.

Programs

Mathematica

nmax = 22; CoefficientList[Series[1/(2 - Exp[-x]/(1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Subfactorial[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

PARI

my(x='x+O('x^25)); Vec(serlaplace(1 / (2 - exp(-x) / (1 - x)))) \\ Michel Marcus, Oct 02 2019

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000166(k) * a(n-k).

a(n) ~ n! * (-LambertW(-exp(-1)/2) / (2*(1 + LambertW(-exp(-1)/2))^(n+2))). - Vaclav Kotesovec, Oct 02 2019