Can you use the inverse Z transform to compute a power series?

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I know one way to compute a power series is to use a Taylor Series and compute derivatives. I'm wondering if you can also do it using the Inverse Z Transform? It looks like yes, but I'm getting stuck in a few places. For example, if I try to use it to get the power series of $z^1$ (the answer should be the $1 z^1 + 0z^2 + 0 z^3 ... $), I get the sequence [1, 1, 1, ...] instead of [1, 0, 0, ...]. It might just be that I'm miscomputing my complex integral.