Assuming I don't know that $S(n,1)=1$ and $S(n,2)=2^{n-1} - 1$, how do I find these numbers? For the first one, the only explanation I can come up with is that a set of n elements can be broken into n partitions that are consisted of one element in only one way. As for the second one, I couldn't really come up with anything.
Any help and comments would be appreciated, thank you :)