Bell number

Bell Numbers, or Bell's Numbers counts the number of ways N objects can be partitioned into groups that are non-empty.

$$B_n$$ can be defined as the following:

$$B_n = \Sigma_{k=0}^{n} S(n,k)$$

where $$S(n,k)$$ is the Stirling Number of the Second Kind. Bell Numbers can also be calculated using Bell's Triangle.