This corresponds to Lisp/Scheme function 'cdr' computed with respect to the lexicographical ordering of parenthesizations/planar binary trees (A014486), i.e. with planar binary trees this is equal to extracting the right subtree (from the root), with general parenthesizations equal to discarding the first sub-parenthesization of the top-level list and with general plane trees equal to discarding the leftmost branch from the root.