My Math Forum Problem with factorial manipulation

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 March 24th, 2014, 05:37 AM #1 Newbie   Joined: Mar 2014 Posts: 1 Thanks: 0 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!
 March 24th, 2014, 06:06 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Problem with factorial manipulation Well, (2n-3)! = (2n)!/(2n * (2n-1) * (2n-2)) so you have $\frac{2(2n-3)!}{n!(n-2)!}=\frac{2(2n)!}{2n\cdot(2n-1)(2n-2)(n-2)!n!}=\frac{(2n)!}{2n\cdot(2n-1)(n-1)!n!}$ 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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