OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
FORMULA
a(n) = Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^(k-1).
a(n) ~ exp(-exp(-1)) * n^(n-1).
MATHEMATICA
CoefficientList[Series[-Exp[-x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[(-1)^(n-k)*Binomial[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]
PROG
(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-exp(-x)*lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 17 2016
STATUS
approved