CZ-SK-MO 2015 Problem 2

Let $A=[0,0]$ and $B=[n,n]$ . In how many ways can we go from $A$ to $B$ , if we always want to go from lattice point to its neighbour (i.e. point with one coordinate the same and one smaller or bigger by one), we never want to visit the same point twice and we want our path to have length $2n+2$ ? (For example, path $[0,0],[0,1],[-1,1],[-1,2],[0,2],[1,2],[2,2],[2,3],[3,3]$ is one of the paths for $n=3$ )