I'm wondering how to find the value of this determinant.
$$\left[ {\begin{array}{*{20}{c}} 0&{{x_1}}&{{x_2}}&{{x_3}}& \ddots &{{x_n}} \\ {{x_1}}&0&{{x_1}}&{{x_2}}&{{x_3}}& \ddots \\ {{x_2}}&{{x_1}}&0&{{x_1}}&{{x_2}}&{{x_3}} \\ {{x_3}}&{{x_2}}&{{x_1}}&0&{{x_1}}&{{x_2}} \\ \ddots &{{x_3}}&{{x_2}}&{{x_1}}&0&{{x_1}} \\ {{x_n}}& \ddots &{{x_3}}&{{x_2}}&{{x_1}}&0 \end{array}} \right]$$
I tried for some small $n$ and couldn't see any clue to find its value expressed by an easy formula. Any help will be appreciated.