Laurent series of $1/(exp(1/x)-1)$

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I have been struggling to find the Laurent series of $$f(z)=\frac{1}{e^{1/z}-1}$$ and its convergence radius as well. Please help me!

It seems to have an essential discontinuity at $z=0$ and $\forall k\in\mathbb{Z}$ some sort of pole at $z=\frac{1}{2\pi i k }$.

Thank you very much expert texperts!