  We derive coupled-cluster equations for three-body Hamiltonians. The
equations for the one- and two-body cluster amplitudes are presented in a
factorized form that leads to an efficient numerical implementation. We employ
low-momentum two- and three-nucleon interactions and calculate the binding
energy of He-4. The results show that the main contribution of the
three-nucleon interaction stems from its density-dependent zero-, one-, and
two-body terms that result from the normal ordering of the Hamiltonian in
coupled-cluster theory. The residual three-body terms that remain after normal
ordering can be neglected.
