A simple combinatorial proof of Shapiro's Catalan convolution
arXiv:1204.5923 · doi:10.1016/j.aam.2012.07.002
Abstract
Shapiro proved an elegant convolution formula involving Catalan numbers of even index. This paper gives a simple combinatorial proof of his formula. In addition, we show that it is equivalent with the alternating convolution formula of central binomial coefficients.