  We derive the 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 $\sqrt{n}$. This is an extension of the classical
Hardy-Ramanujan formula and Szekeres' formula. The proof relies on the saddle
point method.
