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

Author

Max Alekseyev, Feb 09 2008

Keywords

• nonn

Crossrefs

Cf. A114938, A137729, A137737, A137749.

Programs

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 *)

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