login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A137730
Number of circular permutations of the multiset {1,1,2,2,...,n,n} (up to rotations) with odd distances between equal elements.
7
1, 1, 7, 72, 1452, 43200, 1814760, 101606400, 7315680960, 658409472000, 72425043734400, 9560105533440000, 1491376463456140800, 271430516305428480000, 57000408424183569945600, 13680098021793595392000000, 3720986661927868408018944000, 1138621918549924531666944000000
OFFSET
1,3
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
KEYWORD
nonn
AUTHOR
Max Alekseyev, Feb 09, 2008
STATUS
approved