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

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


 * $\displaystyle x^{\underline n} = \sum_k \left({-1}\right)^{n - k} \left[{n \atop k}\right] x^k$

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

Also see

 * Equivalence of Definitions of Unsigned Stirling Numbers of the First Kind


 * Definition:Stirling's Triangles


 * Definition:Stirling Numbers of the Second Kind