The log-convexity of a class of linear recurrence sequences

Abstract

In this paper, we consider the sequences $\{F(n,k){\}}_{n\ge k}$ ($k\ge 1$) defined by$F(n,k)=(n–2)F(n–1,k)+F(n–1,k–1),F(n,1)=\frac{n!}{2},F(n,n)=1.$ We mainly study the log-convexity of $\{F(n,k)\}n\ge k$ ($k\ge 1$) when $k$ is fixed. We prove that $\{F(n,3)\}n\ge 3,\{F(n,4)\}n\ge 5,$ and $\{F(n,5)\}n\ge 6$ are log-convex. In addition, we discuss the log-behavior of some sequences related to $F(n,k)$.
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