Cardinality of Set of Surjections/Examples/m=n+2

Example of Cardinality of Set of Surjections
Let $S$ and $T$ be finite sets.

Let $\card S = m, \card T = n$.

Let $C$ be the number of surjections from $S$ to $T$. Let $m = n + 2$.

Then:
 * $C = \dfrac {n \paren {3 n + 1} \paren {n + 2}!} {24}$

Proof
From Cardinality of Set of Surjections:


 * $C = n! \displaystyle {n + 1 \brace n}$

where $\displaystyle {n + 1 \brace n}$ denotes a Stirling number of the second kind.