For any integer n≥1, we consider a set P2n of 2n points placed equidistantly on a circle. A perfect matching on this point set is comprised of n (straight-line) segments whose endpoints constitute P2n. Let Mn denote the set of all non-crossing perfect matchings on P2n. A perfect matching M∈Mn is said to be centrally symmetric, if it is invariant under point reflection at the circle center. Determine, as a function of n, the number of centrally symmetric perfect matchings within Mn.Proposed by Mirko Petrusevski combinatoricscirclecentral symmetryperfect matchingsymmetry