Recursive actions for scalar theories

We introduce a class of self-interacting scalar theories in which the various coupling contants obey a recursive relation. These imply a particularly simple form for the generating function of the Feynman amplitudes with vanishing external momenta, as well as for the effective potential. In addition we discuss an interesting duality inherent in these models. Specializing to the case of zero spacetime dimensions we find intriguing nullification properties for the amplitudes.