Cool!

On another note, the Bell numbers have a very nice description as coefficients of a power series:

$$\sum_{n=0}^\infty \frac{B_n}{n!} x^n = e^{e^x-1}$$

The best proof uses category theory, namely Joyal's theory of [combinatorial species](https://en.wikipedia.org/wiki/Combinatorial_species), which are functors from the groupoid of finite sets to itself.