  For lambda phi^4 models, the introduction of a large field cutoff improves
significantly the accuracy that can be reached with perturbative series but the
calculation of the modified coefficients remains a challenging problem. We show
that this problem can be solved numerically, and in the limits of large and
small field cutoffs, for the ground state energy of the anharmonic oscillator.
For the two lowest orders, the approximate formulas obtained in the large field
cutoff limit extend unexpectedly far in the low field cutoff region. For the
higher orders, the transition between the small field cutoff regime and the
large field cutoff regime can be described in terms of a universal function.
