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%I #19 Dec 07 2018 16:38:14
%S 1,2,6,22,94,462,2606,16862,124782,1048990,9921550,104447550,
%T 1211190638,15329157278,210093682254,3097760346238,48869022535726,
%U 821007386273118,14630266558195214,275575669958063678,5469996402416702958,114107289124208861470
%N Number of signed permutations of length n avoiding (-2, 1) and (2, -1).
%C Also the number of signed permutations of length 2*n invariant under Dbar and avoiding (-1, 2) and (1, -2).
%C Also the number of signed permutations of length 2*n invariant under R180bar and avoiding (-1, 2) and (1, -2).
%F a(0) = 1, and for n > 0, a(n) = n! + Sum_{j=0..n-1} (n-j)! * a(j).
%F a(n) is the sum of top row terms of M^n, M = an infinite square production matrix as follows:
%F 1, 1, 0, 0, 0, 0,...
%F 2, 0, 2, 0, 0, 0,...
%F 3, 0, 0, 3, 0, 0,...
%F 4, 0, 0, 0, 4, 0,...
%F 5, 0, 0, 0, 0, 5,...
%F ... The upper left term of M^n = A051296(n). - Gary W. Adamson, Sep 26 2011
%e For n = 2, the 6 permutations are (2, 1), (-2, -1), (1, 2), (1, -2), (-1, 2), and (-1, -2).
%e a(3) = 22 = sum of top row terms of M^3 = (11 + 3 + 2 + 6); where 11 = A051296(3).
%p b := proc(n) option remember; if n = 0 then 2 else
%p add(factorial(k)*b(n-k), k=1..n) fi end:
%p a := n -> if n = 0 then return 1 else b(n) end:
%p seq(a(n), n=0..21); # _Peter Luschny_, Dec 07 2018
%Y Cf. A051296.
%K nonn
%O 0,2
%A _Andy Hardt_, Aug 04 2011
%E More terms from _Joerg Arndt_, Aug 16 2011.
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