## For a combinatorial proof of a symmetric identity

In my paper Supercongruences involving dual sequences [Finite Fields Appl. 46(2017), 179-216], I gave a new symmetric identity which states that if x+y=−1 then \sum_{k=0}^n(-1)^k\binom xk^2\binom{y+z}{n-k}=\sum_{k=0}^n(-1)^k\binom yk^2\binom{x+z}{n-k}. (See (1.17) of the paper.) QUESTION: Is there a combinatorial proof of the above symmetric identity? Answer AttributionSource : Link , Question Author : Zhi-Wei Sun , Answer … Read more