Definition:Stirling Numbers of the Second Kind/Definition 1

Definition
Stirling numbers of the second kind are defined recursively by:


 * $\displaystyle {n \brace k} := \begin{cases}

\delta_{n k} & : k = 0 \text{ or } n = 0 \\ & \\ \displaystyle {n - 1 \brace k - 1} + k {n - 1 \brace 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 Stirling Numbers of the Second Kind


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the First Kind