Answer to Question #12768 in Combinatorics | Number Theory for Michael

Question

Calculate sum over permutations \tau(i,j): let $x\in R_{2n}$
$\sum_{\tau(i,j)}(x_i-x_j)^2(a(i,j))^2.$

If a(i,j)=1 if j<=n<i; equal to -1 if i<=n<j, equal 0 otherwise.