Bell Number

A Bell number indicates the number of ways to partition a set.

It is denoted by Bn where n is the cardinality of the set.

Example:

Let S={1,2,3}, n = |S| = 3

The partitions are

1. ∅,{1,2,3}

2. {1},{2,3}

3. {1,2},{3}

4. {1,3},{2}

5. {1},{2},{3}

hence, B3 = 5