Definition:Stirling Numbers of the Second Kind/Definition 2

Definition
Stirling numbers of the second kind are defined as the coefficients $\ds {n \brace k}$ which satisfy the equation:


 * $\ds x^n = \sum_k {n \brace k} x^{\underline k}$

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