Enumeration of vexillary involutions which are equal to their mirror/complement

Vexillary permutations are very important for the study of Schubert polynomials which are involved in several areas of mathematics and physics. In this note we determine the number of n-length vexillary involutions, that is 2143-avoiding involutions, which are equal to their mirror/complement by establishing a bijection with n-length left factors of Motzkin words.