The 2-log-convexity of the Apéry numbers
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- by William Y. C. Chen and Ernest X. W. Xia PDF
- Proc. Amer. Math. Soc. 139 (2011), 391-400 Request permission
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
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Additional Information
- William Y. C. Chen
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- MR Author ID: 232802
- 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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 391-400
- MSC (2010): Primary 05A20; Secondary 11B37, 11B83
- DOI: https://doi.org/10.1090/S0002-9939-2010-10575-0
- MathSciNet review: 2736323