Stirling number

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There are two kinds of Stirling numbers: Stirling numbers of the first kind and Stirling numbers of the second kind. They appear in many combinatoric problems.


Stirling Numbers of the First Kind

Counts the number of permutations of n elements with exactly k cycles.


Stirling Numbers of the Second Kind

Counts the number of partitions of {1, 2, . . . n} into exactly k subsets.