# 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

## 1 Answer

If Hans Lundmark is right, you could see Wikipedia on the Catalan numbers, where the generating function is given under "Proof of the Formula" There are also many references in OEIS

-