Mathematics

How to prove $$\lim\limits_{n\to\infty}\frac{n^{\frac{m-1}2}\sum_{k=0}^m\left(C_n^k\right)^m}{2^{nm}}=\left(\frac2\pi\right)^{\frac m2}\sqrt{\frac\pi{2m}}.$$

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Calculation of limit

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