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Certain matrices of interesting determinant

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up vote 5 down vote favorite 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 share | cite | improve this question asked 4 hours ago T. Amdeberhan 16.9k 2 28 124 5 ...