How do you find the partial fraction decomposition of $$\frac{x^{2m-1}}{\prod\_{k=1}^{n} (x^{2}+k^{2})} \, ,$$ where $m$ is some positive integer? 

I don't know how to approach this other than to find the decomposition for different values of $m$ and $n$ and try to notice a pattern.

Is there a more systematic way I can approach this?