English

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}
}
R2 v1 2026-06-21T20:55:07.525Z