OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..380
FORMULA
a(n) = n! * [x^n] exp(n*x*Sum_{k>=1} x^k/k).
a(n) = (-1)^n*n! * Sum_{k=0..n} n^(n-k)*Stirling1(k,n-k)/k!.
a(n) ~ n^n / (sqrt(1 - (1-s)*(2-s)*s) * exp(n) * s^n * (1-s)^(s*n - 1)), where s = 0.530402312512063468084914246777198746... is the root of the equation (1-s)*(2 + s + s*log(1-s)) = 1. - Vaclav Kotesovec, Aug 30 2018
MATHEMATICA
Table[n! SeriesCoefficient[1/(1 - x)^(n x), {x, 0, n}], {n, 0, 20}]
Join[{1}, Table[(-1)^n n! Sum[n^(n - k) StirlingS1[k, n - k]/k!, {k, n}], {n, 20}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 30 2018
STATUS
approved