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%I #9 Jul 20 2019 01:15:58
%S 1,1,2,6,24,120,480,3600,23040,221760,1895040,22176000,235791360,
%T 3242695680,41153495040,649729382400,9572600217600,170530956288000,
%U 2858960008396800,56707673547571200,1065538430749900800,23283629822509056000,484535856895701811200
%N Number of permutations of 1..n with no adjacent pair summing to n+5.
%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 = 5; 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