Stirling Number of the Second Kind

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Stirling Number of the Second Kind counts the number of way a set of N elements can be partitioned into K nonempty sets.

Stirling Number of the Second Kind can be computed by:

S(n,k)={\frac  {1}{k!}}\Sigma _{{i=0}}^{{k-1}}(-1)^{i}(_{i}^{k})(k-i)^{n}

or the recurrences:

S(n,k)=S(n-1,k-1)+kS(n-1,k)

S(n,k)=\Sigma _{{m=k}}^{n}k^{{n-m}}S(m-1,k-1)