Definition:Stirling Numbers of the Second Kind/Definition 2

Definition
Stirling numbers of the second kind are defined as the coefficients $\displaystyle \left\{ {n \atop k}\right\}$ which satisfy the equation:


 * $\displaystyle x^n = \sum_k \left\{ {n \atop k}\right\} x^{\underline k}$

where $x^{\underline k}$ denotes the $k$th falling factorial of $x$.

Also see

 * Equivalence of Definitions of Stirling Numbers of the Second Kind


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the First Kind