Article ID Journal Published Year Pages File Type
6419750 Advances in Applied Mathematics 2012 6 Pages PDF
Abstract

Shapiro proved an elegant convolution formula involving Catalan numbers of even index. This paper gives a combinatorial proof of his formula. In addition, we show that it is equivalent to an alternating convolution formula of central binomial coefficients.

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Physical Sciences and Engineering Mathematics Applied Mathematics
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A combinatorial proof of Shapiroʼs Catalan convolution
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