A137730 Number of circular permutations of the multiset {1,1,2,2,...,n,n} (up to rotations) with odd distances between equal elements.

1, 1, 7, 72, 1452, 43200, 1814760, 101606400, 7315680960, 658409472000, 72425043734400, 9560105533440000, 1491376463456140800, 271430516305428480000, 57000408424183569945600, 13680098021793595392000000, 3720986661927868408018944000, 1138621918549924531666944000000

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Formula

For even n, a(n) = n!^2 / (2n). For odd n, a(n) = (n!^2 + n!) / (2n).

a(1) = 1; For n > 1: a(n) = Sum_{j=0..n-1} (abs((n - 1)! - n!*Stirling1(n - 1, j)))/2. - Detlef Meya, Apr 10, 2024

Mathematica

a[1]=1; a[n_]:=Sum[Abs[(n-1)!-n!*StirlingS1[n-1, j]], {j, 0, n-1}]/2; Flatten[Table[a[n], {n, 1, 18}]] (* Detlef Meya, Apr 10, 2024 *)

Crossrefs

Cf. A114938, A137729, A137737, A137749.

Sequence in context: A203473 A197951 A221161 * A157920 A321077 A080794

Adjacent sequences: A137727 A137728 A137729 * A137731 A137732 A137733

Keyword

nonn

Author

Max Alekseyev, Feb 09, 2008

Status

approved