I believe this is a variation of related questions. Define a falling exponent of a factorial $n!$ to be $1^{n!} \times 2^{n!-1} \times 3^{n!-2} \times \dots \times n!^1$. Thus for $n=3$ you get $1^6 \* 2^5 \* 3^4 \* 5^2 \* 6^1=24883200$.

* One could solve by doing all the multiplication.
* One could solve by adding the logs.
* One could find an estimation similar to Stirling's for factorials.

Do you think an accurate estimation formula can be found?