Binomial Coefficients $ {\frac{-1}{2} \choose n}$

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i am trying to solve Exercises from Martin Aigner A Copurse in Enummarations, i am having problems with this one: img

I got the first part(well you open the factorials by definition and put the 2's in the right positions, then close), but I am clueless where to start on the second one.