# Stirling Number of the Second Kind

Stirling Number of the Second Kind counts the number of way a set of ${\displaystyle N}$ elements can be partitioned into ${\displaystyle K}$ nonempty sets.
${\displaystyle S(n,k)={\frac {1}{k!}}\Sigma _{i=0}^{k-1}(-1)^{i}(_{i}^{k})(k-i)^{n}}$
${\displaystyle S(n,k)=S(n-1,k-1)+kS(n-1,k)}$
${\displaystyle S(n,k)=\Sigma _{m=k}^{n}k^{n-m}S(m-1,k-1)}$