A simple combinatorial proof of Shapiro's Catalan convolution
Combinatorics
2013-01-16 v1
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.
Cite
@article{arxiv.1204.5923,
title = {A simple combinatorial proof of Shapiro's Catalan convolution},
author = {Gábor V. Nagy},
journal= {arXiv preprint arXiv:1204.5923},
year = {2013}
}