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 A159721 #33 Aug 12 2025 07:31:45
%S A159721 6,36,192,960,4608,21504,98304,442368,1966080,8650752,37748736,
%T A159721 163577856,704643072,3019898880,12884901888,54760833024,231928233984,
%U A159721 979252543488,4123168604160,17317308137472,72567767433216,303465209266176,1266637395197952,5277655813324800
%N A159721 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
%H A159721 R. H. Hardin, <a href="/A159721/b159721.txt">Table of n, a(n) for n = 2..100</a>
%H A159721 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-16).
%F A159721 a(n) = (copies*n)*(copies+1)^(n-2), here: copies = 3.
%F A159721 From _Colin Barker_, Mar 23 2018: (Start)
%F A159721 G.f.: 6*x^2*(1 - 2*x) / (1 - 4*x)^2.
%F A159721 a(n) = 8*a(n-1) - 16*a(n-2) for n>3. (End)
%F A159721 E.g.f.: 3*x*exp(4*x)/4. - _G. C. Greubel_, Jun 01 2018
%F A159721 From _Amiram Eldar_, May 16 2022: (Start)
%F A159721 Sum_{n>=2} 1/a(n) = (16/3)*log(4/3) - 3/2.
%F A159721 Sum_{n>=2} (-1)^n/a(n) = (16/3)*log(5/4) - 7/6. (End)
%t A159721 LinearRecurrence[{8,-16}, {6,36}, 30] (* or *) Table[3*n*4^(n-2), {n, 2, 30}] (* _G. C. Greubel_, Jun 01 2018 *)
%o A159721 (PARI) for(n=2,30, print1(3*n*4^(n-2), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%o A159721 (Magma) [3*n*4^(n-2): n in [2..30]]; // _G. C. Greubel_, Jun 01 2018
%Y A159721 Cf. A159715, A159727, A159733, A159736, A159738, A159739, A159740.
%K A159721 nonn,easy
%O A159721 2,1
%A A159721 _R. H. Hardin_, Apr 20 2009