Chains of semidualizing modules

Let (R, m, k) be a commutative Noetherian local ring. We study the suitable chains of semidualizing R-modules. We prove that when R is Artinian, the existence of a suitable chain of semidualizing modules of length n = max{i >= 0 | m(i) not equal 0} implies that the Poincare series of k and the Bass series of R have very specific forms. Also, in this case, we show that the Bass numbers of R are strictly increasing. This gives an insight into the question of Huneke about the Bass numbers of R.