Definition:Stirling Numbers of the First Kind/Signed/Definition 1

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


 * $\map s {n, k} := \begin{cases}

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

Also see

 * Equivalence of Definitions of Unsigned Stirling Numbers of the First Kind
 * Equivalence of Definitions of Signed Stirling Numbers of the First Kind


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the Second Kind