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

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


 * $\displaystyle \left[{n \atop k}\right] := \begin{cases}

\delta_{n k} & : k = 0 \text{ or } n = 0 \\ & \\ \displaystyle \left[{n - 1 \atop k - 1}\right] + \left({n - 1}\right) \left[{n - 1 \atop k}\right] & : \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 Stirling Numbers of the First Kind


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the Second Kind