A Bijection for the Convolution of Central Binomial Coefficients

Report ID: 
1999-16
Authors: 
Omer Egecioglu
Date: 
1999-05-01 05:00:00

Abstract

Let $A_n = {2n \\choose n }$ for $ n \\geq 0$ denote the the $n$-thelement in the axis of symmetry of the Pascal triangle. The generatingfunction for $A_n$ is $ (1-4t)^{-1/2}$, from which it follows that $ A_0 A_n + A_1 A_{n-1} + \\cdots + A_n A_0 = 4^n $. This note describes a bijective proof of this identity based on lattice paths.

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