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J.Adell and P.Jodra (2008) and S. Koumandos (2013) showed, respectively, that the sequences $\\{\\theta_{n}\\}_{n \\geq 0}$ and $\\{4/135 - n \\cdot (\\theta_{n}- 1/3 )\\}_{n \\geq 0}$ are completely monotone. 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