I have worked out that the Laurent series for $\left(z^4sin(\frac{1}{z}) + (z+1)^4sin(\frac{1}{z+1})\right)$ is given by:

$$\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} \left( \frac{1}{z^{2n-3}} + \frac{1}{(z+1)^{2n-3}} \right)$$

I want to know the residue of the function at $0$ and $-1$. However I'm confused how to find this as the series is not of the normal form $$\sum_{n=-\infty}^\infty a_n(z-z_0)^n$$ How do I calculate these residues?


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