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%I #10 Jul 19 2019 15:20:39
%S 1,1,2,6,12,72,336,2640,17760,175680,1543680,18385920,199019520,
%T 2771112960,35611269120,567422392320,8437755432960,151385755852800,
%U 2556188496691200,50989753530777600,963558923688345600,21152552961009254400,442230750973683302400
%N Number of permutations of 1..n with no adjacent pair summing to n+3.
%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. [proved by William Keith]
%F k = 3; a(n,k) = Sum_{j=0..m} (-2)^j*binomial(m,j)*(n-j)! where m = max(0, floor((n-k+1)/2)). [_Max Alekseyev_, on the Sequence Fans Mailing List]
%K nonn
%O 0,3
%A _R. H. Hardin_, Feb 26 2010
%E More terms from _Alois P. Heinz_, Jan 09 2017
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