Suppose we have a (2m-1) by (2m-1) matrix as following: $$(C_{2j-i}^{2m})_{i,j=1}^{2m-1}.$$ Here $C_p^q$ is defined to be $\frac{q!}{p!(q-p)!}.$ Can any one tell me how to prove it's non singular?
If the following matrix is nonsingular?
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