Factorial of Sum of Natural Numbers Given natural numbers $x,y$, are there some  identities between to $(x+y)!$, $x!$, $y!$, and some sum of "mixed" terms with $x$ and $y$? Essentially, is there a nice expansion of the terms if one were to expand,
$(x+y)!=(x+y)(x+y-1)\,\cdots\,(x+y-k)\,\cdots\,2\cdot1$
I can't seem to find anything relevant. I am open to generalizations to the gamma function if such identities exist in this more general context.

That's pretty broad... the only naturally useful fact I can think of is that $x!y!\mid (x+y)!$, and their quotient is the binomial coefficient $\binom{x+y}{x}=\binom{x+y}{y}$.
