OFFSET
0,4
FORMULA
E.g.f.: Sum_{k>=0} (1 - exp(-k * x))^k / k^k.
MATHEMATICA
a[n_] := Sum[k! * (-k)^(n - k) * StirlingS2[n, k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0] (* Amiram Eldar, Jun 30 2022 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*(-k)^(n-k)*stirling(n, k, 2));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (1-exp(-k*x))^k/k^k)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 30 2022
STATUS
approved