Factorial as Product of Three Factorials

Theorem
This general pattern can be used to find a factorial which is the product of three factorials:
 * $\left({\left({n!}\right)!}\right)! = n! \left({n! - 1}\right)! \left({\left({n!}\right)! - 1}\right)!$

while there are instances of factorials which do not fit that pattern.