Falling and rising factorials

The falling factorial [math]\displaystyle{ (n)_k }[/math] is a multiplication of progressively smaller terms starting with n where there are k number of terms. Each term is a natural number and decreases by 1.

Similarly the rising factorial [math]\displaystyle{ n^{(k)} }[/math]is a multiplication of progressively larger terms starting with n where there are k number of terms. Each term is a natural number and increases by 1.