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!~



Combinatorial proof of a recurrence for the Catalan numbers
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>


