I am trying to figure out if the following expression
$$\frac{(n^2 - n)! }{ n! ((n-1)!)^n }$$
is an integer for all positive integer $n.$
I tried the induction, but induction case is running into problem. So I was looking at it from permutation/combination problems. But so far, couldn't come up with a convincing argument.
Does anybody has any thoughts on this to share ?
Thank you very much.