Sun's curious identity

In combinatorics, Sun's curious identity is the following identity involving binomial coefficients, first established by Zhi-Wei Sun in 2002:



(x+m+1)\sum_{i=0}^m(-1)^i\dbinom{x+y+i}{m-i}\dbinom{y+2i}{i} -\sum_{i=0}^{m}\dbinom{x+i}{m-i}(-4)^i=(x-m)\dbinom{x}{m}. $$

Proofs
After Sun's publication of this identity in 2002, five other proofs were obtained by various mathematicians:


 * Panholzer and Prodinger's proof via generating functions;
 * Merlini and Sprugnoli's proof using Riordan arrays;
 * Ekhad and Mohammed's proof by the WZ method;
 * Chu and Claudio's proof with the help of Jensen's formula;
 * Callan's combinatorial proof involving dominos and colorings.