The 2-log-convexity of the Apery Numbers
Combinatorics
2010-09-14 v3 Number Theory
Abstract
We present an approach to proving the 2-log-convexity of sequences satisfying three-term recurrence relations. We show that the Apery numbers, the Cohen-Rhin numbers, the Motzkin numbers, the Fine numbers, the Franel numbers of order 3 and 4 and the large Schroder numbers are all 2-log-convex. Numerical evidence suggests that all these sequences are k-log-convex for any possibly except for a constant number of terms at the beginning.
Cite
@article{arxiv.0912.0795,
title = {The 2-log-convexity of the Apery Numbers},
author = {William Y. C. Chen and Ernest X. W. Xia},
journal= {arXiv preprint arXiv:0912.0795},
year = {2010}
}
Comments
10 pages; to appear in Proc. Amer. Math. Soc