Definition:Stirling Numbers of the Second Kind/Definition 1

Definition
Stirling numbers of the second 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\} + k \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 Second Kind


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the First Kind