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%I #9 Apr 10 2024 09:13:18
%S 1,2,3,5,12,17,65,80,473,527,4444,4679,51391,52628,703659,711449,
%T 11098896,11156477,197809793,198299024,3927270089,3931960343,
%U 85908742132,85958728847,2052375195679,2052960568556,53160174898371,53167638586121,1483752628890840,1483855482962885,44391655829672177
%N Number of signed permutations of length n invariant under the reverse complement and avoiding (-2, -1), (-2, 1), (2, -1).
%F a(2k) = 2^k k! + \sum_{j=0}^{k-1}(k-j-1)! a(2j)
%F a(2k+1) = (2^k + 1)k! + \sum_{j=0}^{k-1}(k-j-1)! a(2j+1)
%e For n = 2, the permutations are (1, 2), (2, 1), (-1, -2), (-2, -1).
%t a[n_] := a[n] = If[EvenQ[n],
%t Sum[a[2j]*(n/2 - j - 1)!, {j, 0, n/2 - 1}] + 2^(n/2)*(n/2)!,
%t Sum[a[2j+1]*((1/2)*(n - 2j - 3))!, {j, 0, (n - 3)/2}] +
%t (2^((n - 1)/2) + 1)*((n - 1)/2)!];
%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 10 2024 *)
%K nonn
%O 0,2
%A _Andy Hardt_, Aug 04 2011
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