Definitions
The original definition of Stirling numbers of the first kind was algebraic. These numbers, usually written s(n, k), are signed integers whose sign, positive or negative, depends on the parity of n − k. Afterwards, the absolute values of these numbers, |s(n, k)|, which are known as unsigned Stirling numbers of the first kind, were found to count permutations, so in combinatorics the (signed) Stirling numbers of the first kind, s(n, k), are often defined as counting numbers multiplied by a sign factor. That is the approach taken on this page.
Most identities on this page are stated for unsigned Stirling numbers. Note that the notations on this page are not universal.
Read more about this topic: Stirling Numbers Of The First Kind
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