Problem and proof proposed by authors.
Another proof, using lattice paths, can be found in Robert A. Sulanke's article, Objects Counted by the Central Delannoy Numbers, The Journal of Integer Sequences, Vol 6, 2003. A proof by polynomials is in Michel Bataille's paper Some Identities about an Old Combinatorial Sum, The Mathematical Gazette, March 2003, pp. 144-8. A slight change in the above proof leads to m ≥ n, a generalization proved by Li Zhou using lattice paths in The Mathematical Gazette.
© 2005 Mathematical Association of America
Benjamin, A.T., & Bataille, M. (2005). Q.954 and A.954, quickie problem and solution. Mathematics Magazine, 78(4): 324, 329.