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.
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.
Version 2.1.8p2
