(In reply to
computer exploration  far from a proof by Charlie)
Actually, since the second half of the computation just duplicates the first half and as I have shown the result is a square, it suffices to compute half of the terms.
Each of these amounts in the case of n=6 to around 7981444995488.94, near enough to 7981444995489. We can do a check by comparing nearby squares (though there are a lot of them, they are quite far apart by this stage):
63703464216000440340358144 7981444995488^2
63703464216016403230349121 7981444995489^2
63703464216032366120340100 7981444995490^2
7981444995489 is closest by far. So for n=6, the result is 63703464216016403230349121. Unfortunately, there is not enough information to calculate the result for n=7 with any exactitude.
Edited on September 19, 2015, 3:21 am

Posted by broll
on 20150919 03:03:04 