The Stirling numbers of the second kind $S(n,k)$ count partitions of $n$ elements into $k$ non-empty subsets and satisfy: $S(n,k) = kS(n-1,k) + S(n-1,k-1)$ with $S(n,0) = 0$ for $n > 0$ and $S(0,0) = 1$. Compute $S(4,2)$.