Rising Factorial as Quotient of Factorials

Theorem
Let $x \in \Z_{\ge 0}$ be a positive integer.


 * $x^{\overline n} = \dfrac {\left({x + n - 1}\right)!} {\left({x - 1}\right)!}$

where $x^{\overline n}$ denotes the $n$th rising factorial power of $x$.