Given a Laurent polynomial $F$ in the variables $\mathbf{t}=(t_1,\dots,t_n)$, let $CT_{\vec{\mathbf{t}}}\,F$ denote its constant term. For example, $CT_{t_1,t_2}((8t_1-\frac1{3t_1t_2})(5t_1t_2+t_2^2+\frac1{t_1})) =\frac43$.
Starting with Freeman Dyson's constant term identity $$CT_{\vec{\mathbf{t}}}\,\,\prod_{1\leq i\neq j\leq n}\left(1-\frac{t_i}{t_j}\right)^{a_i} =\binom{a_1+\cdots+a_n}{a_1,\dots,a_n},$$ the literature is flooded with even more general conjectures, including Macdonald's list related to root systems. It was not easy (for me) to find a coherent and all-inclusive survey or collection of most relevant constant term formulas. This forces me to ask:
QUESTION. Can you compute the below constant term evaluation? $$CT_{\vec{\mathbf{t}}}\,\, \prod_{i=1}^n\left(1-\frac1{t_i}\right)^{2n}(1+t_i)\cdot \prod_{i<j}^{1,n}\left(1-\frac{t_j}{t_i}\right)\left(1-\frac{t_i}{t_j}\right)(1-t_it_j).$$
