Certain matrices of interesting determinant
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Let $M_n$ be the $ntimes n$ matrix with entries $$binom{i}{2j}+binom{j}{2i}, qquad text{for $1leq i,jleq n$}.$$ QUESTION. Is this true? There is some evidence. The determinant $det(M_{2n+1})=0$ and $$det(M_{2n})=(-1)^nbinom{2n}n^22^{n(n-3)}.$$
linear-algebra determinants elementary-proofs
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asked 4 hours ago
T. Amdeberhan
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