  Recently, it has been proved that a nonlinear quantum oscillator,
generalization of the isotonic one, is exactly solvable for certain values of
its parameters. Here we show that the Schroedinger equation for such an
oscillator can be transformed into a confluent Heun equation. We give a very
simple and efficient algorithm to solve it numerically, no matter what the
values of the parameters are. Algebraic quasi-polynomial solutions, for
particular values of the parameters, are found.
