Let hk(n,r) be the number of ways that r objects out of a limitless supply of objects, distinguishable only by their colors, can be distributed onto k points of a circle, given that objects of each color occur on at most one point, and counting only once arrangements that differ only by cyclic permutation of the points. The numbers h2(n,r) arise naturally in the study of the response of a nonlinear transducer to a sum of incommensurate sinusoids. For the general hk(n,r), a recurrence relation, a generating function, and explicit expressions are determined.