Is there a name for $\frac{n!}{m!}$?

Question

Is there a name or short way of writing of $\frac{n!}{m!}$? I've searched and the closest I could find was binomial coefficient. Is there any other way?

Answer 1

That tends to be called a falling or rising factorial, and there are multiple notations, though none of them are standard enough that you could use one in a paper without defining it first.

Answer 2

One way that I've seen is $(n)_m$. This is a common way to write this notion in combinatorics.