Definition:Stirling Numbers of the First Kind/Unsigned

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 defined as
Some sources do not introduce the signed Stirling numbers of the first Kind, and therefore refer to these as just the Stirling numbers of the first kind.

Also see

 * Definition:Stirling's Triangles


 * Definition:Signed Stirling Numbers of the First Kind
 * Definition:Stirling Numbers of the Second Kind
 * Definition:Pascal's Triangle