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arXiv · 1204.5923

A simple combinatorial proof of Shapiro's Catalan convolution

Gábor V. Nagy
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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.

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Gábor V. Nagy. 2012-04-26. A simple combinatorial proof of Shapiro's Catalan convolution. https://doi.org/10.1016/j.aam.2012.07.002

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