  We derive recursively the perturbation series for the ground-state energy of
the D-dimensional anharmonic oscillator and resum it using variational
perturbation theory (VPT). From the exponentially fast converging approximants,
we extract the coefficients of the large-D expansion to higher orders. The
calculation effort is much smaller than in the standard field-theoretic
approach based on the Hubbard-Stratonovich transformation.
