The Stirling numbers of the first kind are the coefficients in the expansion
where (a Pochhammer symbol) denotes the falling factorial,
Note that (x)0 = 1 because it is an empty product. Combinatorialists also sometimes use the notation for the falling factorial, and for the rising factorial.
(Confusingly, the Pochhammer symbol that many use for falling factorials is used in special functions for rising factorials.)
The unsigned Stirling numbers of the first kind,
(with a lower-case "s"), count the number of permutations of n elements with k disjoint cycles.
Read more about this topic: Stirling Number
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