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A271213 a(n) = 2^(n-2) * (n! + floor(n/2)!) 1
1, 1, 3, 14, 104, 976, 11616, 161472, 2582016, 46451712, 929003520, 20437463040, 490498375680, 12752940072960, 357082301399040, 10712468463943680, 342798990185594880, 11655165645170933760, 419585963202371911680, 15944266600833991311360, 637770664032408384307200 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(n) is the number of rearrangement patterns, i.e., the number of rearrangement map equivalence classes.
REFERENCES
J. Burns, Counting a Class of Signed Permutations and Chord Diagrams related to DNA Rearrangement, Preprint.
LINKS
FORMULA
a(n)=2^(n-2)*(n!+floor(n/2)!)
a(n)~(pi*n/8)^(1/2) (2n/e)^n
EXAMPLE
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}
MATHEMATICA
Table[2^(n-2)*(n!+Floor[n/2]!), {n, 10}]
CROSSREFS
Partition of A000165 into equivalence classes.
Sequence in context: A054202 A084420 A163882 * A167017 A051106 A246731
KEYWORD
nonn,easy
AUTHOR
Jonathan Burns, Apr 02 2016
STATUS
approved

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Last modified April 16 10:35 EDT 2024. Contains 371709 sequences. (Running on oeis4.)