OFFSET
0,2
FORMULA
a(n) ~ n^n / (sqrt(1+LambertW(-exp(-1)/2)) * exp(n) * (-LambertW(-exp(-1)/2))^n). - Vaclav Kotesovec, Sep 01 2024
MAPLE
gf := n -> (1/2 - exp(-x))^n:
ser := n -> series(gf(n), x, 20):
a := n -> expand(2^n*n!*coeff(ser(n), x, n)):
seq(a(n), n = 0..18);
MATHEMATICA
Table[2^n * n! * SeriesCoefficient[(1/2 - E^(-x))^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 01 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 01 2024
STATUS
approved