Let f (x) be a trinomial (i.e., an irreducible polynomial with three terms), denote
by alpha a root of f (x). f (x) is called monogenic, if alpha generates a power integral
basis in K = Q(alpha).There is an extensive literature of monogenic trinomials. A
natural question is to ask if K has power integral bases, different from the one generated
by alpha. In the present paper we consider this question in a special infinite parametric
family of trinomials. Our purpose is to describe all generators of power integral
bases in the number fields generated by the roots of the trinomials.