Thanks so much for the reply. The purpose of constructing a symmetry function is to verify an equation for Vandermonde determinant. For example, n=2 case below, symmetrize a will be equal to b.
Delta[n_] = Product[x[i] - x[j], {i, n}, {j, i - 1}]
a = 2! Delta[2] Product[x[i]^(i - 1), {i, 2}] // Expand
b = Delta[2]^2 // Expand
