Does anyone know what this notation means: $n^{\underline{n}}$?

Question

This is what I don't understand: $n^{\underline{n}}$

This is in a Combinatorics paper I am working my way through, and n is some natural number. I think that it should mean $n!$

The full question is "True or False: The number of permutations of n objects is $n^{\underline{n}}$"

Can anyone confirm this?

Answer 1

I imagine it's the falling factorial:

$$ x^{\underline{n}} = x (x-1)^{\underline{n-1}} \qquad x^{\underline{0}} = 1$$

In particular, $n^{\underline{n}} = n!$ for any nonnegative integer $n$, as you conjectured.