Parabolic Kazhdan-Lusztig polynomials of type −1 for quasi-minuscule quotients

We prove the conjectures of F. Brenti, P. Mongelli and P. Sentinelli which give a combinatorial interpretation to the parabolic Kazhdan-Lusztig polynomials of type −1 for quasi-minuscule quotients of the Weyl groups of type Bn and Dn.