A numerical program is described for calculating the probability distribution of neutrons or delayed neutron precursors in a multiplying assembly. The program obtains the probability distribution generating function, from which the distribution itself is found by inversion of a Laplace transform. Six groups of delayed neutrons may be used. The prompt neutron lifetime is arbitrary and neutron source and reactivity may be functions of time. The existence of an asymptotic probability distribution at late times is proved for constant reactivity. Six group results are shown to be in good agreement with experimental data from Godiva.