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    How to prove that catalan number is (1/n+1)(2nCn)
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    (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?
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    (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.
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    (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?
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    (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.
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    (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
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    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.
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    (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
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    (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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