%I #11 Mar 31 2012 10:32:05
%S 2,10,90,966,12338,181470,3018082,55995486,1146939010,25716746430,
%T 626755197698,16502357651966,466944932413442,14133259249586174,
%U 455715081098876418,15596665064842012158,564724372634695925762,21568978799171323200510,866674159679235417061378,36548294282449538711357438
%N Number of simple symmetric permutations of degree 2n (or 2n+1).
%C A permutation is simple if the only intervals that are fixed are the singletons and [1..m].
%C A permutation p is symmetric if i+j=m+1 implies p(i)+p(j)=m+1.
%C For example the permutations
%C 1234 and 12345
%C 2413 25314
%C are both simple and symmetric.
%C Symmetric simple permutations of degree 2n+1 correspond to simple permutations in the Weyl group of type B_n.
%C Symmetric simple permutations of degree 2n correspond to simple permutations in the Weyl group of type C_n.
%C These occur in pairs so all entries in this sequence will be even.
%H R. Dewji, I. Dimitrov, A. McCabe, M. Roth, D. Wehlau and J. Wilson,
%H <a href="http://arxiv.org/abs/1110.5880">Decomposing Inversion Sets of Permutations and Applications to Faces of the Littlewood-Richardson Cone</a>, arXiv:1110.5880v1[math.CO]
%e The simple symmetric permutations of lowest degree are 2413, 3142, 25314, 41325.
%Y Cf. A111111.
%K nonn
%O 2,1
%A _David Wehlau_, Oct 24 2011