BALTIC-WAY 2009 Problem 16

A $n$ -trønder walk is a walk starting at $(0, 0)$ , ending at $(2n, 0)$ with no self intersection and not leaving the first quadrant, where every step is one of the vectors $(1, 1)$ , $(1, -1)$ or $(-1, 1)$ . Find the number of $n$ -trønder walks.