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In this paper, for the Catalan-Larcombe-French sequence \( \{P_n\}_{n\geq0} \) and the Fennessey-Larcombe-French sequence \( \{V_n\}_{n\geq0} \), we mainly discuss the log-behavior of some sequences related to \( \{P_n\}_{n\geq0} \) and \( \{V_n\}_{n\geq0} \). For example, we study the log-behavior of some sequences such as \( \{P_n^2\}_{n\geq0} \), \( \{n!nV_n\}_{n\geq1} \), \( \{n!V_n\}_{n\geq0} \), and \( \{V_n-P_n\}_{n\geq2} \). In addition, we discuss the monotonicity of some sequences involving \( \{P_n\}_{n\geq0} \) and \( \{V_n\}_{n\geq0} \).