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%I #6 Nov 07 2016 09:02:34
%S 1,1,3,14,104,976,11616,161472,2582016,46451712,929003520,20437463040,
%T 490498375680,12752940072960,357082301399040,10712468463943680,
%U 342798990185594880,11655165645170933760,419585963202371911680,15944266600833991311360,637770664032408384307200
%N a(n) = 2^(n-2) * (n! + floor(n/2)!)
%C a(n) is the number of rearrangement patterns, i.e., the number of rearrangement map equivalence classes.
%D J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.
%H J. Burns, <a href="http://jtburns.myweb.usf.edu/tables/rearrangement_maps.html">Table of Rearrangement Maps and Patterns for n = 1, 2, and 3</a>.
%F a(n)=2^(n-2)*(n!+floor(n/2)!)
%F a(n)~(pi*n/8)^(1/2) (2n/e)^n
%e For n=1 the a(1)=1 solution is the equivalence class {+1,-1}.For n=2 the a(2)=3 solutions are the equivalence classes {+1+2, -2-1}, {+1-2, +2-1, -2+1, -1+2}, and {+2+1, -1-2}
%t Table[2^(n-2)*(n!+Floor[n/2]!),{n,10}]
%Y Partition of A000165 into equivalence classes.
%Y Cf. A271214, A271216, A271217.
%K nonn,easy
%O 0,3
%A _Jonathan Burns_, Apr 02 2016
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