  We study the singular cohomology of the moduli space of rank 2 parabolic
bundles on a Riemann surface where the weights are all 1/4. We give a formula,
based on work of Boden, for the Poincar\'e polynomial of this moduli space in
general, and deduce a complete set of relations in the cohomology ring for the
case when the genus is zero. These relations are recursive in the number of
parabolic points (which must be odd), and are analogous to the relations
appearing in the cohomology ring for the non-parabolic story, which are
recursive in the genus. Our methods use techniques from a paper of Weitsman to
reduce to a linear algebra problem, which we then solve using the theory of
orthogonal polynomials and a continued fraction expansion for the generating
function of the Euler numbers.
