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 A243869 #33 Jun 21 2024 15:35:49
%S A243869 1,5,20,70,231,735,2290,7040,21461,65065,196560,592410,1782691,
%T A243869 5358995,16098830,48340180,145107921,435498525,1306845100,3921234350,
%U A243869 11765101151,35298099655,105899891370,317710858920,953154946381,2859509578385,8578618213640
%N A243869 Expansion of x^4/[(1+x)*Product_{k=1..3} (1-k*x)].
%C A243869 The number of ways to partition a set of n people around a circular table into 4 affinity groups with no two members of a group seated next to each other [Knuth].
%C A243869 The first two primes of the sequence are a(5) and a(96). - _Bruno Berselli_, Jun 13 2014
%H A243869 G. C. Greubel, <a href="/A243869/b243869.txt">Table of n, a(n) for n = 4..1000</a>
%H A243869 J. R. Britnell and M. Wildon, <a href="http://arxiv.org/abs/1507.04803">Bell numbers, partition moves and the eigenvalues of the random-to-top shuffle in types A, B and D</a>, arXiv 1507.04803 [math.CO], 2015.
%H A243869 D. E. Knuth and O. P. Lossers, <a href="http://www.jstor.org/stable/27642185">Partitions of a circular set</a>, Problem 11151 in Amer. Math. Monthly 114 (3), (2007), p 265, E_4.
%H A243869 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-5,6).
%F A243869 a(n) - 3*a(n-1) = A000975(n-3).
%F A243869 From _Bruno Berselli_, Jun 13 2014: (Start)
%F A243869 G.f.: x^4/(1 - 5*x + 5*x^2 + 5*x^3 - 6*x^4).
%F A243869 a(n) = ( 3^n - 4*2^n + (-1)^n + 6 )/24. (End)
%F A243869 a(n) = 5*a(n-1) - 5*a(n-2) - 5*a(n-3) + 6*a(n-4). - _Wesley Ivan Hurt_, May 27 2021
%F A243869 a(n) = Sum_{i=0..n-1} Stirling2(i,3)*(-1)^(i+n-1). (See _Peter Bala_'s original formula at A105794 dated Jul 10 2013.) - _Igor Victorovich Statsenko_, May 31 2024
%t A243869 Table[(3^n - 4 2^n + (-1)^n + 6)/24, {n, 4, 30}] (* _Bruno Berselli_, Jun 13 2014 *)
%o A243869 (Magma) [(3^n-4*2^n+(-1)^n+6)/24: n in [4..30]]; // _Bruno Berselli_, Jun 13 2014
%o A243869 (PARI) for(n=4,50, print1(( 3^n - 4*2^n + (-1)^n + 6 )/24, ", ")) \\ _G. C. Greubel_, Oct 11 2017
%Y A243869 Cf. A000975 (3 affinity groups).
%Y A243869 Column k=4 of A261139.
%K A243869 nonn,easy
%O A243869 4,2
%A A243869 _R. J. Mathar_, Jun 13 2014