OFFSET
0,2
FORMULA
a(n) = n! * [x^n] exp( x/(1-x)^n ) / (1-x).
a(n) = Sum_{k=0..n} (n*k+n-k)!/(n*k)! * binomial(n,k).
log(a(n)) ~ n*(2*log(n) - log(log(n)) - 1 - log(2) + (log(log(n)) + log(2) + 1/2)/log(n)). - Vaclav Kotesovec, Mar 17 2023
MATHEMATICA
Table[Sum[Binomial[n, k]*(n*k + n - k)!/(n*k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 17 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (n*k+n-k)!/(n*k)!*binomial(n, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 17 2023
STATUS
approved