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Q: combinatorics identity ( No Answer,   0 Comments )
Question  
Subject: combinatorics identity
Category: Science > Math
Asked by: math_combinatorics-ga
List Price: $15.00
Posted: 01 May 2006 11:49 PDT
Expires: 02 May 2006 08:57 PDT
Question ID: 724438
I would like to have a proof of the following identity:
\binomial{2n+1-i}{n+1} =
\sum_{j=1}^{n}[(-1)^{n+j} \binomial{n+j-i}{j}\binomial{n}{j-1}]
for all i  1<=i<=n.

note 1: \binomial{n}{k} = n!/(k!(n-k)!)
note 2: Many potentially useful binomial identities can be found in
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete
Mathematics.
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