find two polynomials whose coefficients form unimodal sequences of positive

integers, yet the sequence of coefficients for the product of the polynomials is not uni-

modal

Find polynomials pm), q(a:) E Z[:1:] with positive coefcients such that, if we write 8 19(3) = 2W" 50 t I W) = 2M9 j_n s+ pom) = 23w then (pg)f_0 and (Qj);_{} are unimodal sequences but (uni-f, is not unimodal. In other words, nd two polynomials whose coefcients form unimodal sequences of positive integers, yet the sequence of coefcients for the product of the polynomials is not uni- modal