Ninth and tenth order virial coefficients for hard spheres in D dimensions

We evaluate the virial coefficients Bk for for hard spheres in dimensions Virial coefficients with k even are found to be negative when This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when . Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 for D = 4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D = 3.