A Note on an American Mathematical Monthly Note

In the Feb. 2011 issue of the American Mathematical Monthly, pp. 175-177, there is a probabilistic proof (by G. Chang and C. Xu) of the identity ∑_{i=0}^{n} \binom{2i}{i}\binom{2n−2i}{n−i} = 4^{n}, and of a generalization. This, and the generalization, follow by extracting the coefficient of x^{n} in ((1 − 4x)^{−1/2})^{2} = (1 − 4x)^{−1} and ((1 − 4x)^{−1/2})^{m} = (1 − 4x)^{−m/2} respectively.

Doron Zeilberger, http://www.math.rutgers.edu/~zeilberg/, Feb. 11, 2011. (Exclusively pub-
lished in http://www.math.rutgers.edu/~zeilberg/pj.html (Personal J. of S.B. Ekhad and D. Zeil-
berger) .)