This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137730 #15 Jun 28 2025 17:52:01
%S A137730 1,1,7,72,1452,43200,1814760,101606400,7315680960,658409472000,
%T A137730 72425043734400,9560105533440000,1491376463456140800,
%U A137730 271430516305428480000,57000408424183569945600,13680098021793595392000000,3720986661927868408018944000,1138621918549924531666944000000
%N A137730 Number of circular permutations of the multiset {1,1,2,2,...,n,n} (up to rotations) with odd distances between equal elements.
%F A137730 For even n, a(n) = n!^2 / (2n). For odd n, a(n) = (n!^2 + n!) / (2n).
%F A137730 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
%t A137730 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 *)
%Y A137730 Cf. A114938, A137729, A137737, A137749.
%K A137730 nonn
%O A137730 1,3
%A A137730 _Max Alekseyev_, Feb 09 2008