Residue of $e^{z+\frac1z}$ at $0$. I am trying to compute
$$\text{Res}\: (e^{z+\frac1z}, 0)$$
and can't get a solvable integral using the definition of a residue.
I already know other ways to compute residues of poles of arbitrary order, but nothing for essential singularities- and I believe this is the case here.

$f(z)=e^{z+\frac{1}{z}}=[1+z+\frac{z^2}{2!}+......][1+\frac{1}{z}+\frac{1}{z^2.2!}+....]$.
$Res[f(z);z=0]=$coefficient of $1/z$ in $f(z)=\sum_{n=0}^{\infty}$$\frac{1}{n!.(n+1)!}$
