OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
FORMULA
For n > 0, a(n) = Sum_{k=1..n} 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[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