  We provide an error bound for approximating the time evolution of N bosons by
a generalized nonlinear Hartree equation. The bosons are assumed to interact
via permutation symmetric bounded many-particle potentials and the initial
wave-function is a product state. We show that the error between the actual
evolution of a single particle derived from tracing out the full N-particle
Schrodinger equation and the solution to the mean field approximate generalized
nonlinear Hartree equation scales as 1/N for all times. Our result is a
generalization of rigorous error bounds previously given for the case of
bounded 2-particle potentials
