Does Poly Exponential Time complexity exist?

Question

Poly-Exponential time complexity. Where $f(x) = n^n$

Are there any algorithms which have this time complexity.

Please list them if they exist. I coined the term myself, and a Google search turned nothing.

Answer 1

The number of permutations of $n$ distinct items is $n! \sim \sqrt{2\pi} n^{n+1/2} e^{-n}$, so consider an algorithm that enumerates all these permutations and spends at most $e^n/\sqrt{n}$ time on each one.