  Recently, an intriguing doping dependence of the exchange energies in the
bilayer manganites $La_{2-2x}Sr_{1+2x}Mn_2O_7$ has been observed in the neutron
scattering experiments. The intra-layer exchange only weakly changed with
doping while the inter-layer one drastically decreased. Here we propose a
theory which accounts for these experimental findings. We argue, that the
observed striking doping dependence of the exchange energies can be attributed
to the evaluation of the orbital level splitting with doping. The latter is
handled by the interplay between Jahn-Teller effect (supporting an axial
orbital) and the orbital anisotropy of the electronic band in the bilayer
structure (promoting an in-plane orbital), which is monitored by the Coulomb
repulsion. The presented theory, while being a mean-field type, describes well
the experimental data and also gives the estimates of the several interesting
energy scales involved in the problem.
