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We prove a double binomial sum identity which differs from most binomial sumidentities in that the summands involve the absolute value function. Theidentity is of interest because it can be used in proofs of lower bounds forthe Hadamard maximal determinant problem. Our proof of the identity uses atwo-variable variant of the method of telescoping sums.

Note on a double binomial sum relevant to the Hadamard maximal determinant problem