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A271216
a(n) = 2^n floor(n/2)!
2
1, 2, 4, 8, 32, 64, 384, 768, 6144, 12288, 122880, 245760, 2949120, 5898240, 82575360, 165150720, 2642411520, 5284823040, 95126814720, 190253629440, 3805072588800
OFFSET
0,2
COMMENTS
Number of symmetric rearrangement maps, i.e., rearrangement maps which satisfy a=a^(AI) and a^A = a^I.
REFERENCES
J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.
FORMULA
a(n) = 2^n floor(n/2)!
EXAMPLE
For n=0 the a(0)=1 solution is { ∅ }
For n=1 the a(1)=2 solutions are { +1, -1 }
For n=2 the a(2)=4 solutions are { +1+2, -2-1, +2+1, -1-2 }
For n=3 the a(3)=8 solutions are { +1+2+3, -3-2-1, +3-2+1, -1+2-3, +3+2+1, -1-2-3, +1-2+3, -3+2-1 }
MATHEMATICA
Table[2^n*Floor[n/2]!, {n, 0, 20}]
CROSSREFS
Sequence in context: A128055 A061285 A194810 * A102000 A372256 A165904
KEYWORD
nonn,easy
AUTHOR
Jonathan Burns, Apr 13 2016
STATUS
approved