I am given the following matrix $A=(a_{ij})_{6 \times 6}$, where $a_{ij}=\sum_{k=1}^{10} x_k^{i+j-2}$.
Remark: If $A=(a_{ij})_{10 \times 10}$ with the same $a_{ij}$ defined above, the answer is very classical, i.e., $\det(A)=\prod_{i<j}(x_i-x_j)^2$. But in my case the matrix size is smaller than 10, so I have no idea.
Clearly that $A$ is a real symmetric matrix consisting of power sum. I am wondering if there is a brief expression for $\det(A)$.
Thanks for any advices.