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 A271213 a(n) = 2^(n-2) * (n! + floor(n/2)!) 1

%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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