A133227 The number of ways of selecting an ordered pair of permutations {P_1,P_2} out of S={1,2..,n} (i)each of length floor function {n/2} (ii)each element of P_1 is less than corresponding element of P_2 (iii) There are no common elements between P_1 and P_2.

1, 3, 15, 15, 105, 105

Offset

1,2

Comments

Select a permutation of length k=floor function{n/2} from a set {1,2...,n). construct a cuboid-1 in k-th dimension. Without replacement find another permutation of same length and construct cuboid-2. Cuboid-1 can be kept within cuboid-2.

Links

Table of n, a(n) for n=1..6.

Formula

a(2n+2)= (1+2n)*a(2n) a(2n+1)= (1+2n)*a(2n) with a(2)=1,a(3)=3

Example

a(3)=3 lists {[1][2]},{[1][3]},{[2][3]}
a(4)=15 lists {[12][34]}, {[21][34]}, {[13][24]}, {[12][35]}, {[21][35]}, {[13][25]}, {[14][35]}, {[24][35]}, {[14][25]}, {[12][45]}, {[21][45]}, {[13][45]}, {[31][45]}, {[23][45]}, {[32][45]}

Crossrefs

Cf. A055634.

Sequence in context: A289459 A257115 A159983 * A237628 A074043 A120467

Adjacent sequences: A133224 A133225 A133226 * A133228 A133229 A133230

Keyword

nonn

Author

Srikanth K S, Oct 13 2007

Extensions

Is this A133221 with a slightly different beginning? - N. J. A. Sloane, Oct 13 2007

Status

approved