OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
FORMULA
For n > 0, a(n) = Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^(k-1) * (n-k)!.
a(n) ~ n^(n-1) / (1+exp(-1)).
MATHEMATICA
CoefficientList[Series[-LambertW[-x]/(1+x), {x, 0, 20}], x] * Range[0, 20]!
Flatten[{0, Table[Sum[(-1)^(n-k) * Binomial[n, k] * k^(k-1) * (n-k)!, {k, 1, n}], {n, 1, 20}]}]
PROG
(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-x)/(1+x)))) \\ G. C. Greubel, Nov 12 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 18 2016
STATUS
approved