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A183766
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1/32 the number of (2n+1)X4 binary arrays with equal numbers of 2X2 subblocks with sum mod two being 0 and 1
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1
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40, 7392, 1555840, 346131968, 79420170240, 18585877094400, 4409408507412480, 1056689477487820800, 255189244398549336064, 62004700939478066266112, 15140238779254079729172480, 3712064235466595220724908032
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