Total Number of Set Partitions/Examples/4

Example of Total Number of Set Partitions
Let $S$ be a set whose cardinality is $4$.

Then the number of partitions of $S$ is $15$.

Proof
Let $\map p n$ denote the cardinality of the set of partitions of a set whose cardinality is $n$.

From Total Number of Set Partitions, $\map p n$ is the $n$th Bell number $B_n$.

Thus: