  The ground-state energy of the Hubbard model on a Bethe lattice with infinite
connectivity at half filling is calculated for the insulating phase. Using
Kohn's transformation to derive an effective Hamiltonian for the
strong-coupling limit, the resulting class of diagrams is determined. We
develop an algorithm for an algebraic evaluation of the contributions of
high-order terms and check it by applying it to the Falicov-Kimball model that
is exactly solvable. For the Hubbard model, the ground-state energy is exactly
calculated up to order t^12/U^11. The results of the strong-coupling expansion
deviate from numerical calculations as quantum Monte Carlo (or density-matrix
renormalization-group) by less than 0.13% (0.32% respectively) for U>4.76.
