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The value of $\sum_{n=2}^{1947}\frac{1}{2^n+\sqrt{2^{1947}}}$ is equal to

If $\binom{30}{1}^{2}+2\binom{30}{2}^{2}+3\binom{30}{3}^{2}+...+30\binom{30}{30}^{2}=\frac{\alpha(60!)}{(30!)^{2}}$ then $\alpha$ is equal to