The matrix I am inquiring about here is the $n \times n$ matrix where the entry $A_{ij}$ is $\frac{1}{(i+j-1)^2}$. The $2 \times 2$ matrix looks like \begin{pmatrix} 1 & 1/4 \\ 1/4 & 1/9 \end{pmatrix}. The $3 \times 3$ case looks like \begin{pmatrix} 1 & 1/4 & 1/9 \\ 1/4 & 1/9 & 1/16 \\ 1/9 & 1/16 & 1/25 \end{pmatrix}. The $n \times n$ matrix looks like \begin{pmatrix} 1 & 1/4 & \cdots & 1/(n^2) \\ 1/4 & 1/9 & \cdots & 1/{(n+1)^2} \\ \vdots & \vdots & \cdots & \vdots \\ 1/(n^2) & 1/{(n+1)^2} & \cdots & 1/{(2n-1)^2} \end{pmatrix}. If anyone has any information or knows of any papers talking about this matrix please let me know. Thanks!

The matrix I am inquiring about here is the $n \times n$ matrix where the entry $A_{ij}$ is $\frac{1}{(i+j-1)^2}$. The $2 \times 2$ matrix looks like $$ \begin{pmatrix} 1 & 1/4 \\ 1/4 & 1/9 \end{pmatrix}. $$ The $3 \times 3$ case looks like $$ \begin{pmatrix} 1 & 1/4 & 1/9 \\ 1/4 & 1/9 & 1/16 \\ 1/9 & 1/16 & 1/25 \end{pmatrix}. $$ The $n \times n$ matrix looks like $$ \begin{pmatrix} 1 & 1/4 & \cdots & 1/(n^2) \\ 1/4 & 1/9 & \cdots & 1/{(n+1)^2} \\ \vdots & \vdots & \cdots & \vdots \\ 1/(n^2) & 1/{(n+1)^2} & \cdots & 1/{(2n-1)^2} \end{pmatrix}. $$ If anyone has any information or knows of any papers talking about this matrix please let me know. Thanks!