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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.

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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
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A must read on generating functions is Wilf's book www.math.upenn.edu/~wilf/gfology2.pdf –  TKN May 13 '11 at 21:26
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@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

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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

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