Suppose an exchangable sequence with values in a nice measurable space $S$ admits a prediction rule of the following form: given the first $n$ terms of the sequence, the next term equals the $j$th distinct value observed so far with probability $p_{j,n}$, for $j = 1,2, \ldots$, and otherwise is a new value with distribution $\nu$ for some probability measure $\nu$ on $S$ with no atoms. Then the $p_{j,n}$ depend only on the partitition of the first $n$ integers induced by the first $n$ values of the sequence. All possible distributions for such an exchangeable sequence are characterized in terms of constraints on the $p_{j,n}$ and in terms of their de Finetti representations.