I'm solving a complexity question where I have:
$$ n!/2^n $$
The goal is to find an upper bound for this.
My idea is using the fact that: $$ n! = O(n^n)$$ $$ n!/2^n = O((n/2)^n) = O(n^n)$$
But is a correct upper bound, and if so is it the tightest upper bound that can be found? I know that n! is asymptotically larger than 2^n, but I'm struggling to do a tighter analysis.