# Find a function for well form brackets using generating functions

How to find a function for calculating the number of well form brackets (for "n" pairs of brackets) using generating function? This is a probably a routine problem for some people, but I haven't got any resource on generating function.

-
What are well formed brackets? A series of parentheses that have the same number of opens as closes? Wouldn't that just be $\binom {2n}{n}$ for a string $2n$ long? – Ross Millikan May 13 '11 at 21:25
A must read on generating functions is Wilf's book www.math.upenn.edu/~wilf/gfology2.pdf – TKN May 13 '11 at 21:26
@Ross: Probably it means that you at any stage must have more left than right brackets, in which case the answer is given by the Catalan numbers. – Hans Lundmark May 13 '11 at 21:30
@Hans: I think you are right. – Ross Millikan May 13 '11 at 21:41