co.combinatorics - Probability of n k-sided dice showing exactly m different faces

I found the following closed form solution for the abovementioned problem:

$${1over k^n}cdot{k!over (k-m)!}cdot{{{nover m}}}$$ with ${{{nover m}}}$ being the Stirling Number of the second kind.

Although it seems to have some intuition and seems to work for a sample problem for which I have the solution this closed form is not from a trusted source. Unfortunately I can't find any other source.

My question: Could anyone acknowledge this closed form solution and/or give me a hint where to find a citable source.