  A systematic nonperturbative scheme is implemented to calculate the ground
state energy for a wide class of strongly correlated fermion models. The scheme
includes: (a) method of automatic calculations of the cumulants of the model
Hamiltonian; (b) method of the ground state energy calculation from these
cumulants using the $t$-expansion proposed by Horn and Weinstein [Phys. Rev. D
\textbf{30}, 1256 (1984)] with new procedure of its extrapolation to
$t\rightarrow\infty$. As an example of application of the method all cumulants
up to the 8-th order for spinless fermion model are calculated exactly, and
converging sequences of approximations to the ground state energy are obtained
for one-, two- and three-dimensional versions of the model.
