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 A159715 #23 May 16 2022 02:45:46
%S A159715 4,18,72,270,972,3402,11664,39366,131220,433026,1417176,4605822,
%T A159715 14880348,47829690,153055008,487862838,1549681956,4907326194,
%U A159715 15496819560,48814981614,153418513644,481176247338,1506290861232,4707158941350
%N A159715 Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
%H A159715 R. H. Hardin, <a href="/A159715/b159715.txt">Table of n, a(n) for n = 2..100</a>
%H A159715 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9).
%F A159715 a(n) = (copies*n)*(copies+1)^(n-2), here: copies = 2.
%F A159715 Apparently a(n) = A027261(n-1), n > 2. - _R. J. Mathar_, Apr 21 2009
%F A159715 Conjectures from _Colin Barker_, Mar 23 2018: (Start)
%F A159715 G.f.: 2*x^2*(2 - 3*x) / (1 - 3*x)^2.
%F A159715 a(n) = 2*3^(n-2)*n for n>1.
%F A159715 a(n) = 6*a(n-1) - 9*a(n-2) for n>3. (End)
%F A159715 E.g.f.: 2*x*exp(3*x)/3. - _G. C. Greubel_, Jun 01 2018
%F A159715 From _Amiram Eldar_, May 16 2022: (Start)
%F A159715 Sum_{n>=2} 1/a(n) = (9/2)*log(3/2) - 3/2.
%F A159715 Sum_{n>=2} (-1)^n/a(n) = 3/2 - (9/2)*log(4/3). (End)
%t A159715 LinearRecurrence[{6,-9}, {}, 30] (* or *) Table[2*n*3^(n-2), {n, 2, 30}] (* _G. C. Greubel_, Jun 01 2018 *)
%o A159715 (PARI) for(n=2, 30, print1(2*n*3^(n-2), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%o A159715 (Magma) [2*n*3^(n-2): n in [2..30]]; // _G. C. Greubel_, Jun 01 2018
%Y A159715 Cf. A027261, A159721, A159727, A159733, A159736, A159738, A159739, A159740.
%K A159715 nonn
%O A159715 2,1
%A A159715 _R. H. Hardin_, Apr 20 2009