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%I #16 Aug 26 2015 02:11:00
%S 1,3,51,131355,131953155208875,5496027066067360087228913484456796875,
%T 27805296606704951937976342299927372748633425216234990144120838935506416477839670037841796875
%N a(n) = (2^(n-1))!*y(n) where y(n)=1/2*(y(n-1))^2+1 for n>=2 and y(1)=1.
%C a(n) is also the number of knockout tournament seedings that satisfy the symmetry property.
%H Alexander Karpov, <a href="http://www.uni-heidelberg.de/md/awi/forschung/dp600.pdf">A theory of knockout tournament seedings</a>, Heidelberg University, AWI Discussion Paper Series, No. 600.
%t Table[(2^(n-1))!*FoldList[(1/2)*(#1)^2+1&,1,Range[2,7]][[n]],{n,1,7}] (* _Ivan N. Ianakiev_, Aug 25 2015 *)
%Y Cf. A067667 (number of seedings).
%K nonn
%O 1,2
%A _Alexander Karpov_, Aug 11 2015