Definition:Stirling Numbers of the First Kind/Signed

Definition
Signed Stirling numbers of the first kind are defined recursively by:


 * $s \left({n, k}\right) = \begin{cases}

\delta_{n k} & : k = 0 \text{ or } n = 0 \\ s \left({n - 1, k - 1}\right) - \left({n - 1}\right) s \left({n - 1, k}\right) & : \text{otherwise} \\ \end{cases}$ where:
 * $\delta_{n k}$ is the Kronecker delta
 * $n$ and $k$ are non-negative integers.

Also see

 * Definition:Stirling's Triangles


 * Definition:Unsigned Stirling Numbers of the First Kind
 * Definition:Stirling Numbers of the Second Kind
 * Definition:Pascal's Triangle