Evaluate: 

$$\sum\_{n=1}^{\infty} \frac{H\_n}{(n+1)^2}$$

A user stated: "most of the time sum up the residues of $(\gamma+\psi(z))^2\cdot r(z)$. To determine the residues, just expand the digamma function as a Laurent series about the positive integers." where $r(z)$ is the rational function.

Firstly, what is the Laurent series of $\psi(z)$??

And how would I find the residues? Any help is appreciated.