$\binom{n}{k}$ is a "binomial coefficient;" $n \; P \; k$ is a "__________." If I want to search for information concerning $\binom{n}{k}$, I can't Google that symbol directly, nor can I search for something like "n C k" and get anything relevant, but because the term "binomial coefficient" exists it's possible to search for, say, "Catalan numbers in terms of binomial coefficients" or whatever. Conversely, if I want to write something involving $\binom{n}{k}$ in a fundamental way and make it discoverable to others' searches, I should make sure to include the term "binomial coefficient."
Is there a similar noun describing the function
$$n \; P \; k = \frac{n!}{(n-k)!}$$
Obviously one could use a rather verbose description, but that's not very useful for searchability -- imagine replacing the search described above with "Catalan numbers in terms of the number of combinations of k elements out of an n element subset," for instance, to which this would be analogous.
The best solution I can see at present is to use the term "binomial coefficient" and maybe rewrite the formula to include an extraneous $k!$ or something.

This is a falling factorial:
$$ (n)_k = n^{\underline k} = \underbrace{n\cdot(n-1)\cdot(n-2)\cdots(n-k+1)}_{k\text{ factors}} = \frac{n!}{(n-k)!} $$
