  The Boros-Moll polynomials arise in the evaluation of a quartic integral. The
original double summation formula does not imply the fact that the coefficients
of these polynomials are positive. Boros and Moll proved the positivity by
using Ramanujan's Master Theorem to reduce the double sum to a single sum.
Based on the structure of reluctant functions introduced by Mullin and Rota
along with an extension of Foata's bijection between Meixner endofunctions and
bi-colored permutations, we find a combinatorial proof of the positivity. In
fact, from our combinatorial argument one sees that it is essentially the
binomial theorem that makes it possible to reduce the double sum to a single
sum.
