Question: Are there any useful forms for the expression $1!\cdot 2!\cdot 3!\cdot ...\cdot n!$? I'm trying to solve a problem that involves this expression and thought it might help to find a more "workable" form for it, but I didn't get very far.

Thanks

Answer: 
A posibble form is: $$\prod\_{i=1}^ni!$$

In other way is $$1^n\cdot2^{n-1}\cdot3^{n-2}\cdot\cdots\cdot(n-1)^2\cdot n^1$$
It is sometimes referred to as the superfactorial of n (although there is at least one other function that's also called superfactorial), and its values are given by [OEIS sequence A000178](http://oeis.org/A000178). I don't believe there are any shortcuts to computing it, other than noting that $sf(n) = \prod\_{1 \le i \lt j \le n}\left( j - i \right)$