I am studying Scott's book Group Theory. In the Exercise $1.1.17$ he asks us to show that if $S$ is a set and $|S|=n$, then there are $n^{\frac{n^{2}+n}{2}}$ commutative binary operations on $S$. But he doesn't talk about how many associative binary operations there are on a finite set.
Is there an answer to that question? I mean, how many associative binary operations there are on a finite set?