Hi everybody,


Does there exist an explicit formula for the Stirling Numbers of the First Kind which are given by the formula
$$
x(x-1)\cdots (x-n+1) = \sum\_{k=0}^n s(n,k)x^k.
$$


Otherwise, what is the computationally fastest formula one knows?



Stirling Number of first kind : Implementation
There is an explicit formula : $s(n,m)=\frac{(2n-m)!}{(m-1)!}\sum\_{k=0}^{n-m}\frac{1}{(n+k)(n-m-k)!(n-m+k)!}\sum\_{j=0}^{k}\frac{(-1)^{j} j^{n-m+k} }{j!(k-j)!}.$ For once, it is not in Wikipedia (en), but in the french version of it (and I posted it there myself, if I may so brag)


