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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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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 …