This seems like it must have been addressed somewhere already, but I cannot find it in any standard series tables.

I have the equation:

$f(z) = \left(1 + \frac{1}{z}\right)^z$.

What is the general form for the $n$th term of the series? That is, if I have

$f(z) \sim \sum_{n=0}^{\infty} \frac{c_n}{z^n}$

near $z = \infty$, what is the form of $c_n$?