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For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.

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Specific partial sum of even/odd binomial coefficients

I have a following sum: $S_g=\sum_{k=0}^g k\binom{4g+2}{2k}$ I can transform it into a different sum $S_g=(2g+1)\sum_{k=1}^g\binom{4g+1}{2k-1}$ What is the closed form or what is the method to dea …
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