2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/20979Exact 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.4 pages, 4 figures, RevTeX, v2: references changed, formatted for PRLStatistical Mechanicstext