  Let $p_{r,s}(n)$ denote the number of partitions of a positive integer $n$
into parts containing no multiples of $r$ or $s$, where $r>1$ and $s>1$ are
square-free, relatively prime integers. We use classical methods to derive a
Hardy-Ramanujan-Rademacher-type infinite series for $p_{r,s}(n)$.
