1 results
On the log-concavity of the sequence
for some combinatorial sequences 
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 4 / August 2018
- Published online by Cambridge University Press:
- 22 June 2018, pp. 881-892
- Print publication:
- August 2018
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- Article
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Recently, Sun posed a series of conjectures on the log-concavity of the sequence
, where is a familiar combinatorial sequence of positive integers. Luca and Stănică, Hou et al. and Chen et al. proved some of Sun's conjectures. In this paper, we present a criterion on the log-concavity of the sequence . The criterion is based on the existence of a function f(n) that satisfies some inequalities involving terms related to the sequence . Furthermore, we present a heuristic approach to compute f(n). As applications, we prove that, for the Zagier numbers 
, the sequences 
are strictly log-concave, which confirms a conjecture of Sun. We also prove the log-concavity of the sequence 
of Cohen–Rhin numbers.
for some combinatorial sequences 
, the sequences 
are strictly log-concave, which confirms a conjecture of Sun. We also prove the log-concavity of the sequence 
of Cohen–Rhin numbers.