Each term must appear only once. With this expansion it is possible to find terms of different order, in terms of the number of particles that are involved. The first term is the non-interaction term (corresponding to no interactions amongst particles), the second term corresponds to the two-particle interactions, the third to the two-particle interactions amongst 4 (not necessarily distinct) particles, and so on. This physical interpretation is the reason this expansion is called the cluster expansion: the sum can be rearranged so that each term represents the interactions within clusters of a certain number of particles.