Dyson’s conjecture was proved independently by Gunson and Wilson . In1970, a brief and elegant proof was published by Good . Later Zeilberger gave acombinatorial proof.The q-analog of Theorem 1.1 was conjectured by Andrews in 1975, and was firstproved, combinatorially, by Zeilberger and Bressoud . Recently, Gessel and Xin gave a different proof by using properties of formal Laurent series.In recent years, there has been increasing interest in evaluating the coefficients ofmonomials M : =bi = 0, in the Dyson product. Based on Good’sproof, Kadell gave three non-constant term coefficients. Sills and Zeilberger de-scribed an algorithm that automatically conjectures and proves closed-form expressions.Later, Sills extended Good’s idea and obtained the closed-form expressions for M being, respectively. By virtue of Zeilberger and Sills’ Maple package GoodDyson,Lv, Xin and Zhou found two closed-form expressions for M that has a square in thenumerator. Moreover, by generalizing Gessel-Xin’s ...