Are there in any relatively efficient known algorithms to compute the partition function $P(n)$ for a given $n$? What's known about the complexity class of this problem as a function of $n$?
Perhaps I'm missing something trivial here, but other than listing some recurrent definitions of this function and some of their asymptotics, I don't see this precise information (complexity class, and known algorithms with their runtime/space complexity) in either of these articles: