I would like to ask whether there is a combinatorial proof of the following recurrence relation for Catalan numbers: $$ C_{n+1}=\frac{4n+2}{n+2} C_n. $$
Thanks!~
I would like to ask whether there is a combinatorial proof of the following recurrence relation for Catalan numbers: $$ C_{n+1}=\frac{4n+2}{n+2} C_n. $$ Thanks!~ 


What you are asking is reported as fourth proof in the wiki article for the formula of the Catalan numbers: http://en.wikipedia.org/wiki/Catalan_number#Fourth_proof 


these papers can you help: 

