Definition:Stirling Numbers of the First Kind/Signed/Definition 2

Definition
Signed Stirling numbers of the first kind are defined as the polynomial coefficients $s \left({n, k}\right)$ which satisfy the equation:


 * $\displaystyle x^{\underline n} = \sum_k s \left({n, k}\right) x^k$

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

Also see

 * Equivalence of Definitions of Stirling Numbers of the First Kind


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the Second Kind