OFFSET
0,4
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
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}]
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(1 / (2 - exp(-x) / (1 - x)))) \\ Michel Marcus, Oct 02 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 01 2019
STATUS
approved