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:

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

$S(n,k) = \Sigma_{m=k}^n k^{n-m} S( m - 1, k - 1 )$