Nice list! The nth item on the list below (starting from n=1) is (n-1)/n! (though I haven't checked all of them). This corresponds for example to the volume of the n-simplex in the n-cube [0,1]^n whose vertices are the origin and the n points whose coordinates are one 0 and the rest 1's. --Dan On 2013-09-26, at 11:47 AM, Charles Greathouse wrote:
So this is basically the Hadamard problem, and the maximum volume of an n-simplex is A003432 (n)/n!:
1 1 2 1/2 3 1/3 4 1/8 5 1/24 6 1/80 7 2/315 8 1/720 9 1/2520 10 1/11340 11 9/246400 12 3/394240 13 3/1971200 14 3/10250240 15 64/638512875 16 2/127702575 17 2/638512875 18 1/1876446000 19 78125/486580401635328 20 90625/3892643213082624
Charles Greathouse Analyst/Programmer Case Western Reserve University