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In this paper, we investigate the properties of Genocchi number {Gn}n 1 . We prove that the sequence {|G2n|}n 1 is log-convex. In addition, we discuss the monotonicity of some sequences related to {Gn}n 1 . In particular, we show that { n √|G2n|}n 1 is strictly increasing and { n+1 √|G2n+2|/ n √|G2n|}n 2 is strictly decreasing.

The log-convexity of Genocchi numbers and the monotonicity of some sequences related to Genocchi numbers