We investigate summing sequences in the context of polynomial hypergroups. It will be shown that the summing sequence (Sn) n∈N 0 , where Sn = {0, 1, . . . , n}, is equivalent to the growth condition (H) of the Haar weights h(n). This condition is also sufficient for the existence of means which satisfy a strong form of translation invariance. Furthermore we give exact representations of the unique translation invariant mean on the space of weakly almost periodic sequences for a large class of polynomial hypergroups.Mathematics Subject Classification (2010). Primary 42C05; Secondary 43A62.