In how many ways can a regular n-gon be divided into $n-2$ triangles if different orientations are not to be counted separately?
I have counted the ways for different n-gons and found that up to a pentagon the answer is 1 but then for $n=6,7,8,9$ the answers are $4,6,19,49$. I'm supposed to express this in terms of the Catalan numbers but don't know how to do that.