[math-fun] Proof on Catalan Numbers

Here is an excerpt from one of my unpublished manuscripts: https://github.com/bradklee/Docs/blob/master/CatalanExcerpt.pdf It describes a derivation of the Catalan numbers, which I have not seen elsewhere. Does this proof work for everyone? Has anyone seen it written down elsewhere? How do you think it compares to using André's reflection method? Thanks --Brad