On anti-pentadiagonal persymmetric Hankel matrices with perturbed corners

In this paper we express the eigenvalues of real anti-pentadiagonal persymmetric Hankel matrices with perturbed corners as the zeros of explicit rational functions. From these prescribed eigenvalues we give an orthogonal diagonalization for these matrices and a formula to compute its integer powers. In particular, an explicit expression not depending on any unknown parameter for the determinant and the inverse of complex anti-pentadiagonal persymmetric Hankel matrices with perturbed corners is provided.