It is shown here on [Mathworld's page on Stirling number of the second kind](http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html) that 


$$
\sum\_{k=1}^n S(n,k) (k-1)! z^k = (-1)^n \text{Li}\_{1-n}(1+\frac{1}{z})
$$


where $S(n,k)$ is Stirling number of the second kind and $\text{Li}\_{1-n}$ is the polylogarithm.


Can somebody provide me some reference on where this identity came from? It isn't shown on Mathworld's page.



The relationship between Stirling number of the second kind and the polylogarithm
See [Steven Landsburg's note.](http://www.thebigquestions.com/dotcom/query.pdf)


