Sum[(-1)^k * (2^n)^(2 * k) / z^(2 * k + 1) , {k, 0, Infinity}] assuming Abs[z] > 2^Re[n]Sum[(-1)^k * (2^n)^(2 * k) / z^(2 * k + 1) , {k, 0, Infinity}] assuming Abs[z] > 2^Re[n]

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