  Based on a two-dimensional extended Hubbard model with electron-phonon
interaction, we have studied the effect of polaron formation on the charge
ordering (CO) transition. It is found that for fully ferromagnetically ordered
spins the CO state may go through a process of appearance, collapse and
reappearance with decreasing temperature. This is entirely due to a
emperature-dependent polaron bandwidth. On the other hand, when a paramagnetic
spin state is considered, only a simple reentrant behavior of the CO transition
is found, which is only partly due to polaron effect. This model is proposed as
an explanation of the observed reentrant behavior of the CO transition in the
layered manganite LaSr$_2$Mn$_2$O$_7$.
