Falling and rising factorials

The falling factorial ${\displaystyle (n)_{k}}$ 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 ${\displaystyle n^{(k)}}$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.