  In a gedankenexperiment N particles in a generalized GHZ-type beam entangled
state (each particle can be in one of M beams) are fed into N symmetric 2M-port
beam splitters (spatially separated). Correlation functions for such a process
(using the Bell numbers value assignment approach) reveal a remarkable
symmetry. For N=M+1 greater or equal to 4 a series of GHZ paradoxes are shown.
