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Symmetry 2019, 11(1), 62; https://doi.org/10.3390/sym11010062

On the Catalan Numbers and Some of Their Identities

1,2
and
2,*
1
School of Mathematics and Statistics, Kashgar University, Xinjiang 844006, China
2
School of Mathematics, Northwest University, Xi’an 710127, Shaanxi, China
*
Author to whom correspondence should be addressed.
Received: 5 December 2018 / Revised: 31 December 2018 / Accepted: 4 January 2019 / Published: 8 January 2019
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)
Full-Text   |   PDF [227 KB, uploaded 8 January 2019]

Abstract

The main purpose of this paper is using the elementary and combinatorial methods to study the properties of the Catalan numbers, and give two new identities for them. In order to do this, we first introduce two new recursive sequences, then with the help of these sequences, we obtained the identities for the convolution involving the Catalan numbers. View Full-Text
Keywords: catalan numbers; elementary and combinatorial methods; recursive sequence; convolution sums catalan numbers; elementary and combinatorial methods; recursive sequence; convolution sums
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Zhang, W.; Chen, L. On the Catalan Numbers and Some of Their Identities. Symmetry 2019, 11, 62.

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