OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
For n > 0, a(n) = (-1)^n*n!+Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^k * (n-k)!.
a(n) ~ n^n / (1+exp(-1)).
a(0) = 1; a(n) = -n*a(n-1) + n^n. - Seiichi Manyama, May 01 2023
MATHEMATICA
CoefficientList[Series[1/(1+LambertW[-x])/(1+x), {x, 0, 20}], x] * Range[0, 20]!
Flatten[{1, Table[(-1)^n*n! + Sum[(-1)^(n-k) * Binomial[n, k] * k^k * (n-k)!, {k, 1, n}], {n, 1, 20}]}]
PROG
(PARI) my(x='x+O('x^50)); Vec(serlaplace(1/((1 + lambertw(-x))*(1+x)))) \\ G. C. Greubel, Nov 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Oct 18 2016
STATUS
approved