On monotonicity of some combinatorial sequences

作者：Qing-Hu Hou, Zhi‐Wei Sun, Haomin Wen · 发表于：Publicationes Mathematicae Debrecen · 年份：2014 · DOI：10.5486/pmd.2014.5817 · 被引用次数：10 · 研究领域：Advanced Combinatorial Mathematics、Advanced Mathematical Identities、Analytic Number Theory Research

We confirm Sun's conjecture that ( n+1 Fn+1/ n Fn ) n 4 is strictly decreasing to the limit 1, where (Fn) n 0 is the Fibonacci sequence. We also prove that the sequence ( n+1 Dn+1/ n Dn ) n 3 is strictly decreasing with limit 1, where Dn is the n-th derangement number. For m-th order harmonic numbers