Enumeration of bilaterally symmetric 3-noncrossing partitions. Schützenberger’s theorem for the ordinary RSK correspondence naturally extends to Chen et. al’s correspondence for matchings and partitions. Thus, the counting of bilaterally symmetric $k$-noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for 3-noncrossing partitions, we use a different technique to develop a {sc Maple} package for 2-dimensional vacillating lattice walk enumeration problems. As an application, we find an interesting relation between two special bilaterally symmetric partitions.