Summary: Involutions and pseudo-involutions in the Riordan group are interesting because of their numerous applications. In this paper we study involutions using sequence characterizations of the Riordan arrays. For a given $B$-sequence we find the unique function $f(z)$ such that the array $(g(z), f (z))$ is a pseudo-involution. As a combinatorial application, we find the interpretation of each entry in the Bell array $(g(z),f(z))$ with a given $B$-sequence.

05A15

pseudo-involution, Riordan group, B-sequence, PI tree