A271216 a(n) = 2^n floor(n/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.

Links

Table of n, a(n) for n=0..20.

J. Burns, Table of Rearrangement Maps and Patterns for n = 1, 2, and 3.

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

Cf. A000165, A271213.

Sequence in context: A128055 A061285 A194810 * A102000 A372256 A165904

Adjacent sequences: A271213 A271214 A271215 * A271217 A271218 A271219

Keyword

nonn,easy

Author

Jonathan Burns, Apr 13 2016

Status

approved