Count the number of paths from $(0,0)$ to $(2n,n)$ than never go above $y=x$
At first I thought of the problem by expanding the graph to $(0,0)$ to $(2n,2n)$ and messing around with adding and subtracting multiples of the Catalan number formula, but I feel this is far too rudimentary and in doing so I am leaving out many paths that move through the $x=n$ to $x=2n$ and $y=0$ to $y=n$ square section of the graph that has no restrictions (because the diagonal cuts off at $(n,n)$). Of course, you can only go right and up.
Thanks!