A generalized Hardy-Ramanujan formula for the number of restricted integer partitions.

We derive an asymptotic formula for p n (N , M) , the number of partitions of integer n with part size at most N and length at most M. We consider both N and M are comparable to n. This is an extension of the classical Hardy-Ramanujan formula and Szekeres' formula. The proof relies on the saddle point method. [ABSTRACT FROM AUTHOR]