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

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


 * $\ds {n \brack k} := \begin{cases}

\delta_{n k} & : k = 0 \text { or } n = 0 \\ & \\ \ds {n - 1 \brack k - 1} + \paren {n - 1} {n - 1 \brack 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


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the Second Kind