  Given a sequence (a_k) = a_0, a_1, a_2,... of real numbers, define a new
sequence L(a_k) = (b_k) where b_k = a_k^2 - a_{k-1} a_{k+1}. So (a_k) is
log-concave if and only if (b_k) is a nonnegative sequence. Call (a_k)
"infinitely log-concave" if L^i(a_k) is nonnegative for all i >= 1. Boros and
Moll 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 about regions of infinite
log-concavity. We investigate related questions about the columns of Pascal's
triangle, q-analogues, symmetric functions, real-rooted polynomials, and
Toeplitz matrices. In addition, we offer several conjectures.
