  Based on computational experiments, Jim Propp and Vic Reiner suspected that
there might exist a sequence of combinatorial objects $X_n$, each carrying a
natural action of the cyclic group $C_{n-1}$ of order $n-1$ such that the
triple $\left(X_n,C_{n-1},\frac{1}{[n+1]_q}{2n \brack n}_q\right)$ exhibits the
cyclic sieving phenomenon. We prove their suspicion right.
