Alternative infinite summations that equal $e$

Question

Everyone (and I mean everyone) knows this sum:

$$\sum_{n=0}^\infty \frac{1}{k!} =e$$ Are there any lesser known infinite sums that go to e?

Answer 1

You can check here, maybe it is what you want : https://en.wikipedia.org/wiki/List_of_representations_of_e

Answer 2

I know this one because of Stirling's formula:

$e = \lim_{n \rightarrow \infty} \frac{n}{\sqrt[n]{n!}}$

Answer 3

Hint: See Dobinski's formula for Bell numbers.