A271213 a(n) = 2^(n-2) * (n! + floor(n/2)!)

1, 1, 3, 14, 104, 976, 11616, 161472, 2582016, 46451712, 929003520, 20437463040, 490498375680, 12752940072960, 357082301399040, 10712468463943680, 342798990185594880, 11655165645170933760, 419585963202371911680, 15944266600833991311360, 637770664032408384307200

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

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-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.

Cf. A271214, A271216, A271217.

Sequence in context: A054202 A084420 A163882 * A167017 A051106 A246731

Adjacent sequences: A271210 A271211 A271212 * A271214 A271215 A271216

Keyword

nonn,easy

Author

Jonathan Burns, Apr 02 2016

Status

approved