A recursion procedure is presented for deriving the dispersion coefficients C-s((k)) of the van der Waals interaction between two atoms in spherically symmetric ground states to arbitrary high orders k of perturbation theory. The complete asymptotic expansion for the dispersion interaction between two ground-state hydrogen atoms up to C-30 (including terms arising from tenth order perturbation theory) are then generated using a pseudo-state expansion for the two atom Green's function. (c) 2005 Elsevier B.V. All rights reserved.