and

Given a sequence (ak) = a0, a1, a2,... of real numbers, define a new se-quence L(ak) = (bk) where bk = a2k − ak−1ak+1. So (ak) is log-concave if and only if (bk) is a nonnegative sequence. Call (ak) infinitely log-concave if Li(ak) is nonnegative for all i ≥ 1. Boros and Moll [4] conjectured that the rows of Pascal’s triangle are infinitely log-concave. Using a computer and a stronger version of log-concavity, we prove their conjecture for the nth row for all n ≤ 1450. We also use our methods to give a simple proof of a recent result of Uminsky and Yeats [30] about regions of infinite log-concavity. We investigate related questions about the columns of Pascal’s triangle, q-analogues, sym-metric functions, real-rooted polynomials, and Toeplitz matrices. In addition, we offer several conjectures