  We study a dilute Bose gas of atoms whose scattering length a is large
compared to the range of their interaction. We calculate the energy density of
the homogeneous Bose-Einstein condensate to second order in the low-density
expansion, expressing it in terms of a and a second parameter Lambda_* that
determines the low-energy observables in the 3-body sector. The second-order
correction to the energy density has a small imaginary part that reflects the
instability due to 3-body recombination. In the case of a trapped Bose-Einstein
condensate with large negative scattering length, we calculate the coefficient
of the 3-body mean-field term in the energy density in terms of a and Lambda_*.
It can be very large if there is an Efimov state near threshold.
