Is there closed form for eigenvalues of this matrix

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What is nice closed expression for determinant and eigenvalues of $$A=\begin{bmatrix} 1&2&\dots&m\\ m&1&\dots&m-1\\ \vdots&\vdots&\ddots&\vdots\\ 2&3&\dots&1 \end{bmatrix}?$$