The log-behavior of some sequences related to the Catalan-Larcombe-French sequence and the Fennessey-Larcombe-French sequence

摘要

In this paper, for the Catalan-Larcombe-French sequence {P_n}_(n≥0) and the Fennessey-Larcombe-French sequence {V_n}_(n≥0), we mainly discuss the log-behavior of some sequences related to {P_n}_(n≥0) and {V_n}_(n≥0). For example, we study the log-behavior of some sequences such as {P_n~2}_(n≥0), {n!nV_n}_(n≥1), {n!V_n}_(n≥0), and {V_n - P_n}_(n≥2). In addition, we discuss the monotonicity of some sequences involving {P_n}_(n≥0) and {V_n}_(n≥0).