

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
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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.


LINKS



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, 21, +2+1, 12 }
For n=3 the a(3)=8 solutions are { +1+2+3, 321, +32+1, 1+23, +3+2+1, 123, +12+3, 3+21 }


MATHEMATICA

Table[2^n*Floor[n/2]!, {n, 0, 20}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



