**S1[n,k]**(Stirling number of the first kind) is the number of permutations of length n containing k cycles, multiplied by the sign of these permutations.

Example:
Permutation Cycles
123 (1)(2)(3)
132 (1)(23)
213 (12)(3)
231 (123)
312 (132)
321 (13)(2)
Thus:
S1[3,1]=2
S1[3,2]=-3
S1[3,3]=1

Stirling Numbers of the first kind are implemented in Mathematica as

**StirlingS1**.

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