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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(2n3)!  n! (n2)! (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, (2n3)! = (2n)!/(2n * (2n1) * (2n2)) so you have and so you want 2n(2n1)(n1)!n! = (n+1)! n! which is 4n2 = n+1 which only happens when n = 1. 

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