OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..266
Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)
FORMULA
a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / (sqrt(LambertW(exp(2)*n)^2 - 1) * exp(n*(1 - 1/LambertW(exp(2)*n))) * LambertW(exp(2)*n)^n). - Vaclav Kotesovec, Feb 20 2022
MATHEMATICA
a[n_] := n!*(1 + Sum[(k*(n - k))^k/k!, {k, 1, n}]); Array[a, 18, 0] (* Amiram Eldar, Feb 19 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, (k*(n-k))^k/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 19 2022
STATUS
approved