OFFSET
0,2
FORMULA
a(n) = (n!)^n * [x^n] exp(x) * Sum_{k>=0} x^k / (k!)^n.
a(n) ~ (2*Pi)^((n-1)/2) * n^(n^2 - n/2 + 1/2) / exp(n*(n-1) - 1/12). - Vaclav Kotesovec, Jul 14 2020
MATHEMATICA
Table[(n!)^n Sum[1/((k!)^n (n - k)!), {k, 0, n}], {n, 0, 10}]
Table[(n!)^n SeriesCoefficient[Exp[x] Sum[x^k/(k!)^n, {k, 0, n}], {x, 0, n}], {n, 0, 10}]
PROG
(PARI) a(n) = (n!)^n * sum(k=0, n, 1 / ((k!)^n * (n-k)!)); \\ Michel Marcus, Jul 14 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 14 2020
STATUS
approved