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 orders and and the large Schroder 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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