Special name for $k!\binom{n}{k}=\frac{n!}{(n-k)!}$

Question

$$\binom{n}{k}=\frac{n!}{k!(n-k)!}$$ The expression above is also known as binomial coefficient. Is there a similar naming convention that describes the one below? $$k!\binom{n}{k}=\frac{n!}{(n-k)!}$$

Answer 1

$\displaystyle \frac{n!}{(n-k)!} = k!\binom{n}{k} = n(n-1)(n-2)\cdots (n-k+1)$ is the falling factorial.

Answer 2

If the choose function is defined as: $$C(n,r)=\frac{n!}{r!(n-r)!}$$ And the permutation function is defined as: $$P(n,r)=\frac{n!}{(n-r)!}$$ then you are looking at the permutation function