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# Catalan numbers watch

1. How to prove that catalan number is (1/n+1)(2nCn)
2. (Original post by Spandy)
How to prove that catalan number is (1/n+1)(2nCn)
I thought that was the definition of a catalan number?
3. (Original post by tombayes)
I thought that was the definition of a catalan number?
Well, about a year ago, my mentor derived it by solving this Q- there are n'+1's and n'-1's are arranged in a series, such that, at any point, the sum from the first term is always non-negative. I was glancing through my notes, but couldn't solve that problem now.
4. (Original post by Spandy)
Q- there are n'+1's and n'-1's are arranged in a series, such that, at any point, the sum from the first term is always non-negative.
that is not a question. Are you trying to show that the nth term in the sequence is the nth Catalan number?
5. (Original post by tombayes)
that is not a question. Are you trying to show that the nth term in the sequence is the nth Catalan number?
Being so long ago, I believe I cannot be expected to remember the exact details, as far as I remember, the total number of possible arrangements was the nth catalan number.
6. (Original post by Spandy)
How to prove that catalan number is (1/n+1)(2nCn)
You're going to need to pick a definition of Catalan number first (that isn't that formula). But most definitions are going to be essentially equivalent.

There are then various derivations of the formula at:

http://en.wikipedia.org/wiki/Catalan...of_the_formula
7. You cant 'prove' a definition, you have gone wrong somewhere at a very basic level.

You are probably wanting to prove that Catalan numbers arise as a solution to some particular problem, which is very different.
8. (Original post by poohat)
You cant 'prove' a definition, you have gone wrong somewhere at a very basic level.

You are probably wanting to prove that Catalan numbers arise as a solution to some particular problem, which is very different.
Yeah, sorry
9. (Original post by DFranklin)
You're going to need to pick a definition of Catalan number first (that isn't that formula). But most definitions are going to be essentially equivalent.

There are then various derivations of the formula at:

http://en.wikipedia.org/wiki/Catalan...of_the_formula
Thanks!

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