Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The 2-log-convexity of the Apéry Numbers


Authors: William Y. C. Chen and Ernest X. W. Xia
Journal: Proc. Amer. Math. Soc. 139 (2011), 391-400
MSC (2010): Primary 05A20; Secondary 11B37, 11B83
Published electronically: September 23, 2010
MathSciNet review: 2736323
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present an approach to proving the 2-log-convexity of sequences satisfying three-term recurrence relations. We show that the Apéry numbers, the Cohen-Rhin numbers, the Motzkin numbers, the Fine numbers, the Franel numbers of orders $ 3$ and $ 4$ and the large Schröder numbers are all 2-log-convex. Numerical evidence suggests that all these sequences are $ k$-log-convex for any $ k\geq 1$ possibly except for a constant number of terms at the beginning.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05A20, 11B37, 11B83

Retrieve articles in all journals with MSC (2010): 05A20, 11B37, 11B83


Additional Information

William Y. C. Chen
Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
Email: chen@nankai.edu.cn

Ernest X. W. Xia
Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
Email: xxw@cfc.nankai.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10575-0
PII: S 0002-9939(2010)10575-0
Keywords: Apéry number, log-convexity, 2-log-convexity, infinite log-convexity.
Received by editor(s): December 4, 2009
Published electronically: September 23, 2010
Additional Notes: The authors wish to thank the referee, Tomislav Došlić, and Tanguy Rivoal for helpful comments
This work was supported by the 973 Project, the PCSIRT Project of the Ministry of Education, and the National Science Foundation of China.
Communicated by: Jim Haglund
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.