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Hankel matrices are square matrices whose coefficients $a_{i,j}$ only depend on the sum $i+j$. They appear in particular in the theory of orthogonal polynomials on the real line.
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Determinant of identity matrix plus Hilbert matrix
I am looking for the determinant
$$ \det(I_n + H_n) $$
where $I_n$ is the $n \times n$ identity matrix and $H_n$ is the $n \times n$ Hilbert matrix, whose entries are given by
$$ [H_n]_{ij} = \frac …