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 May 23rd, 2009, 01:13 PM #1 Member   Joined: Jan 2009 Posts: 95 Thanks: 0 Binomial and Beta Things to prove: 1) $\sum_{j=1}^n{j {n \choose j} {2n \choose j}}=\frac{1}{\beta(2n,n)}$ http://www.research.att.com/~njas/seque ... ge=english 2) $\sum_{j=0}^n{ { 2n-1 \choose j} {n \choose j} }=\frac{1}{n \beta(2n,n)}$ 3) $\sum_{j=0}^n{ {n \choose j} ^2}=\frac{4^n}{n \beta(n,\frac{1}{2})}$
 May 23rd, 2009, 04:41 PM #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: Binomial and Beta Do you have Maple? Zeilberger's A=B programs would probably make short work of those: http://www.math.rutgers.edu/~zeilberg/programsAB.html

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