For a nonnegative integer n, let \(F_n(x)=\sum_{m=0}^n \frac{(-2)^m (2n-m)! \Gamma(x+1)}{m! (n-m)! \Gamma(x-m+1)}\). Find all x such that F_n(x)=0.

The best solution was submitted by Bumsu Kim (김범수), 수리과학과 2010학번.

Here is his Solution of Problem 2011-21.