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 A151651 #14 Sep 13 2022 02:21:10
%S A151651 0,225,15606,554931,16689816,477537957,13457517066,377519524263,
%T A151651 10576236506508,296179535707065,8293376986582302,232217254675249371,
%U A151651 6502103768266128576,182059062180981345549,5097654923210293555314,142734346723080681522255
%N A151651 Number of permutations of 6 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.
%H A151651 Andrew Howroyd, <a href="/A151651/b151651.txt">Table of n, a(n) for n = 1..500</a>
%H A151651 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (45,-570,2822,-5481,4557,-1372).
%F A151651 a(n) = 28^n - (6*n + 1)*7^n + 3*n*(6*n + 1). - _Andrew Howroyd_, May 06 2020
%F A151651 From _Colin Barker_, Jul 18 2020: (Start)
%F A151651 G.f.: 9*x^2*(25 + 609*x - 2121*x^2 - 2401*x^3) / ((1 - x)^3*(1 - 7*x)^2*(1 - 28*x)).
%F A151651 a(n) = 45*a(n-1) - 570*a(n-2) + 2822*a(n-3) - 5481*a(n-4) + 4557*a(n-5) - 1372*a(n-6) for n>6. (End)
%F A151651 From _G. C. Greubel_, Sep 12 2022: (Start)
%F A151651 a(n) = Sum_{j=0..2} (-1)^j*binomial(6*n+1, j)*binomial(8-j, 6)^n.
%F A151651 E.g.f.: exp(28*x) - (1 + 42*x)*exp(7*x) + 3*x*(7 + 6*x)*exp(x). (End)
%t A151651 Table[Sum[(-1)^j*Binomial[6*n+1, j]*Binomial[8-j, 6]^n, {j,0,2}], {n, 30}] (* _G. C. Greubel_, Sep 12 2022 *)
%o A151651 (PARI) a(n) = {28^n - (6*n + 1)*7^n + 3*n*(6*n + 1)} \\ _Andrew Howroyd_, May 06 2020
%o A151651 (PARI) concat(0, Vec(9*x^2*(25 + 609*x - 2121*x^2 - 2401*x^3) / ((1 - x)^3*(1 - 7*x)^2*(1 - 28*x)) + O(x^20))) \\ _Colin Barker_, Jul 18 2020
%o A151651 (Magma) [(&+[(-1)^j*Binomial(6*n+1, j)*Binomial(8-j, 6)^n: j in [0..2]]): n in [1..30]]; // _G. C. Greubel_, Sep 12 2022
%o A151651 (SageMath)
%o A151651 def A151651(n): return sum((-1)^j*binomial(6*n+1, j)*binomial(8-j, 6)^n for j in (0..2))
%o A151651 [A151651(n) for n in (1..30)] # _G. C. Greubel_, Sep 12 2022
%Y A151651 Column k=2 of A237252.
%K A151651 nonn,easy
%O A151651 1,2
%A A151651 _R. H. Hardin_, May 29 2009
%E A151651 Terms a(7) and beyond from _Andrew Howroyd_, May 06 2020