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%I #7 Jan 13 2014 12:49:35
%S 1,1,2,6,24,120,720,5040,30240,282240,2338560,26853120,280143360,
%T 3802982400,47638886400,745007155200,10872058982400,192275074252800,
%U 3200021920972800,63107717389516800,1178953777845043200,25641537378199142400,531103116540719923200
%N Number of permutations of 1..n with no adjacent pair summing to n+7.
%C If a(n,k) is the number of permutations of 1..n with no adjacent pair summing to n+k, then a(n,k) = a(n,k+1) for n+k even.
%F k = 7; m = max(0,floor((n-k+1)/2)); a(n,k) = Sum_{j=0..m} (-2)^j C(m,j) (n-j)!.
%K nonn
%O 0,3
%A _R. H. Hardin_, Feb 26 2010, comment proved by _William J. Keith_, formula from _Max Alekseyev_, on the Sequence Fans Mailing List