A general density expansion method based on the calculus of finite differences (Ramshaw J. D., J. Chem. Phys., 57 (1972) 2070) is revisited and reformulated. The original expression for the coefficients in the expansion is transformed into an alternative equivalent form which simplifies and facilitates their evaluation. The use of the method is illustrated by determining the virial coefficients of arbitrary order in a density expansion of the pressure in a classical monatomic gas. The resulting virial coefficients are expressed in terms of the Ursell reducible cluster integrals. The functional form of those expressions is determined by simple recursion relations.