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Partial Vandermonde circulant determinant expression
Consider following partial Vandermonde type, circulant matrix
$\begin{bmatrix}
x_1 & x_2 & 0 & \dots & 0 & x_n\\
x_1^2 & x_2^2 & x_3^2 & \dots & 0 & 0\\
\vdots ...
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