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The Boros-Moll sequence $\\{d_i(m)\\}_{i=0}^m$ arises in the study of evaluation of certain quartic integral, and a lot of interesting inequalities for this sequence have been obtained. In this paper we show that the Boros-Moll sequence $\\{d_i(m)\\}_{i=0}^m$, its normalization $\\{d_i(m)/i!\\}_{i=0}^m$, and its transpose $\\{d_i(m)\\}_{m\\ge i}$ satisfy the Briggs inequality. 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