A combinatorial proof of Shapiro%26apos;s Catalan convolution

作者：Nagy Gabor V^*

来源：Advances in Applied Mathematics, 2012, 49(3-5): 391-396.

DOI：10.1016/j.aam.2012.07.002

• Catalan numbers
• Shapiro convolution

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.

• 出版日期2012-10