  Exact results are given for the fourth virial coefficient of hard spheres in
even dimensions up through 12. The fifth and sixth virial coefficients are
numerically computed for dimensions 2 through 50 and it is found that the sixth
virial coefficient is negative for D >= 6. Numerical studies are made of the
contributing Ree Hoover diagrams up to order 17. It is found for D >= 3 that
for large order a class of diagrams we call "loose packed" dominates and the
rate of growth of these diagrams is used to study bounds on the radius of
convergence.
