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A271213
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a(n) = 2^(n-2) * (n! + floor(n/2)!)
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1
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1, 1, 3, 14, 104, 976, 11616, 161472, 2582016, 46451712, 929003520, 20437463040, 490498375680, 12752940072960, 357082301399040, 10712468463943680, 342798990185594880, 11655165645170933760, 419585963202371911680, 15944266600833991311360, 637770664032408384307200
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of rearrangement patterns, i.e., the number of rearrangement map equivalence classes.
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REFERENCES
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J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.
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LINKS
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FORMULA
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a(n)=2^(n-2)*(n!+floor(n/2)!)
a(n)~(pi*n/8)^(1/2) (2n/e)^n
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EXAMPLE
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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}
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MATHEMATICA
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Table[2^(n-2)*(n!+Floor[n/2]!), {n, 10}]
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CROSSREFS
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Partition of A000165 into equivalence classes.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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