OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..253
FORMULA
a(n) ~ exp(1/2) * (n!)^2.
E.g.f.: Sum_{k>=0} k! * (-log(1-x))^k. - Seiichi Manyama, Apr 22 2022
MATHEMATICA
Table[Sum[Abs[StirlingS1[n, k]]*k!^2, {k, 0, n}], {n, 0, 20}]
PROG
(PARI) a(n) = sum(k=0, n, k!^2*abs(stirling(n, k, 1))); \\ Michel Marcus, Oct 14 2018
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, k!*(-log(1-x))^k))) \\ Seiichi Manyama, Apr 22 2022
(Magma) [(&+[Abs(StirlingFirst(n, k))*(Factorial(k))^2: k in [0..n]]): n in [0..20]]; // G. C. Greubel, Oct 14 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 13 2018
STATUS
approved