Lower order terms for the moments of symplectic and orthogonal families of L-functions

We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet L-functions, L(1/2,χd), and also of the L-functions associated to quadratic twists of an elliptic curve over Q. In so doing, we are led to study determinants of binomial coefficients of the form .