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March 24th, 2014, 05:37 AM   #1
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Problem with factorial manipulation

I'm working on a catalan number identity proof, but having problems with the formula on the top (which is a catalan identity, checked thoroughly) and manipulating that formula to the formula on the bottom, which is the standard formula for catalan numbers. having trouble with factorial manipulation..


2(2n-3)!
----------
n! (n-2)!


(2n)!
----------
(n+1)! n!
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March 24th, 2014, 06:06 AM   #2
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Re: Problem with factorial manipulation

Well, (2n-3)! = (2n)!/(2n * (2n-1) * (2n-2)) so you have


and so you want 2n(2n-1)(n-1)!n! = (n+1)! n! which is 4n-2 = n+1 which only happens when n = 1.
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