Abstract:  Based on the recurrence relations on the coefficients of the Boros-Moll polynomials P_m(a) = ∑_i d_i(m)aⁱ derived independently by Kauers and Paule, and Moll, we are led to the discovery of the reverse ultra log-concavity of the sequence {d_i(m)}. We also show that the sequence {i!d_i(m)} is log-concave for m ≥ 1. Two conjectures are proposed.

  AMS Classification:  05A20; 33F10

  Keywords:  log-concavity, reverse ultra log-concavity, upper bound, imaginary roots, Boros-Moll polynomials

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