Remebering bell numbers

Question

I read about Bell numbers and I'm looking for a way to generate these numbers quickly for tests and exams. I know there is a recursively relation but it is not useful for big numbers .

Answer 1

You can calculate them rapidly by using the bell triangle.

Answer 2

The exponential generating function of the Bell numbers is $e^{e^{x}-1}$, that is, the coefficient of $x^n/n! $ in the power series expansion of $e^{e^{x}-1}$ is the number of partitions of a set of $n $ elements.

You would like to see Section 1.6 in Generating Functionology by Herbert.S.Wilf for more information. Hope it helps.