Algorithm for finding all paths in a NxN grid

Question

Imagine a robot sitting on the upper left hand corner of an NxN grid. The robot can only move in two directions: right and down. How many possible paths are there for the ro

Answer 1

https://math.stackexchange.com/questions/104032/finding-points-in-a-grid-with-exactly-k-paths-to-them - look here at my solution. Seems that it is exactly what you need (yes, statements are slightly different, but in general case they are just the same).