# 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.