The 2-log-convexity of the Apéry Numbers
- Autores: William Y. C. Chen, Ernest X.W. Xia
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 139, Nº 2, 2011, págs. 391-400
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10575-0
- Enlaces
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Resumen
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 and and the large Schröder numbers are all 2-log-convex. Numerical evidence suggests that all these sequences are -log-convex for any possibly except for a constant number of terms at the beginning.
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