OFFSET
0,4
FORMULA
E.g.f.: Sum_{k>=0} log(1 + k*x)^k / k^k.
MATHEMATICA
a[0] = 1; a[n_] := Sum[k! * k^(n-k) * StirlingS1[n, k], {k, 1, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 03 2022 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*k^(n-k)*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k*x)^k/k^k)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 03 2022
STATUS
approved