OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
a(n) = Sum_{k=0..n-1} (-1)^k * binomial(n,k)^2 * k! * (n - k)^(n - k - 1).
a(n) ~ (1 - exp(-1))^(n + 3/2) * n^(n-1). - Vaclav Kotesovec, Jan 26 2020
MATHEMATICA
nmax = 21; CoefficientList[Series[-LambertW[-x/(1 + x)]/(1 + x), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k Binomial[n, k]^2 k! (n - k)^(n - k - 1), {k, 0, n - 1}], {n, 0, 21}]
PROG
(PARI) seq(n)={Vec(serlaplace(-lambertw(-x/(1 + x) + O(x*x^n)) / (1 + x)), -(n+1))} \\ Andrew Howroyd, Jan 25 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jan 25 2020
STATUS
approved