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 A151647 #16 Sep 12 2022 03:21:11
%S A151647 0,100,5925,167475,3882250,84320250,1791011475,37753995925,
%T A151647 793816473600,16676797204500,350257183908625,7355694727665975,
%U A151647 154471515733316550,3243914368665860350,68122282848892857375,1430568461732082827625,30041941039388979651100
%N A151647 Number of permutations of 5 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.
%H A151647 Andrew Howroyd, <a href="/A151647/b151647.txt">Table of n, a(n) for n = 1..500</a>
%H A151647 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (36,-390,1720,-3165,2556,-756).
%F A151647 a(n) = 21^n - (5*n + 1)*6^n + 5*n*(5*n + 1)/2. - _Andrew Howroyd_, May 06 2020
%F A151647 From _Colin Barker_, Jul 18 2020: (Start)
%F A151647 G.f.: 25*x^2*(4 + 93*x - 273*x^2 - 324*x^3)/((1 - x)^3*(1 - 6*x)^2*(1 - 21*x)).
%F A151647 a(n) = 36*a(n-1) - 390*a(n-2) + 1720*a(n-3) - 3165*a(n-4) + 2556*a(n-5) - 756*a(n-6) for n>6. (End)
%F A151647 From _G. C. Greubel_, Sep 12 2022: (Start)
%F A151647 a(n) = Sum_{j=0..2} (-1)^j*binomial(5*n+1, j)*binomial(7-j, 5)^n.
%F A151647 E.g.f.: exp(21*x) - (1 + 30*x)*exp(6*x) + (5/2)*x*(6 + 5*x)*exp(x). (End)
%t A151647 LinearRecurrence[{36,-390,1720,-3165,2556,-756},{0,100,5925,167475,3882250, 84320250}, 30] (* _Harvey P. Dale_, Nov 01 2021 *)
%o A151647 (PARI) a(n) = {21^n -(5*n+1)*6^n +5*n*(5*n+1)/2} \\ _Andrew Howroyd_, May 06 2020
%o A151647 (PARI) concat(0, Vec(25*x^2*(4 + 93*x - 273*x^2 - 324*x^3) / ((1 - x)^3*(1 - 6*x)^2*(1 - 21*x)) + O(x^20))) \\ _Colin Barker_, Jul 18 2020
%o A151647 (Magma) [(&+[(-1)^j*Binomial(5*n+1, j)*Binomial(7-j, 5)^n: j in [0..2]]): n in [1..30]]; // _G. C. Greubel_, Sep 12 2022
%o A151647 (SageMath)
%o A151647 def A151647(n): return sum((-1)^j*binomial(5*n+1, j)*binomial(7-j, 5)^n for j in (0..2))
%o A151647 [A151647(n) for n in (1..30)] # _G. C. Greubel_, Sep 12 2022
%Y A151647 Column k=2 of A237202.
%K A151647 nonn,easy
%O A151647 1,2
%A A151647 _R. H. Hardin_, May 29 2009
%E A151647 Terms a(8) and beyond from _Andrew Howroyd_, May 06 2020