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 A151603 #14 Sep 08 2022 08:45:38 %S A151603 0,80,1395,12560,96575,698940,4897655,33590720,226746135,1511651900, %T A151603 9976916015,65303466480,424472551295,2742745738460,17631936915975, %U A151603 112844396291840,719383026394055,4570198050070620,28944587650489535,182807922003138800,1151689908619826415 %N A151603 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order. %H A151603 Andrew Howroyd, <a href="/A151603/b151603.txt">Table of n, a(n) for n = 1..500</a> %H A151603 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-75,145,-120,36). %F A151603 a(n) = n*((5/2)*6^n - 25*n) for n > 1. - _Andrew Howroyd_, May 04 2020 %F A151603 From _Colin Barker_, Jul 17 2020: (Start) %F A151603 G.f.: 5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2). %F A151603 a(n) = 15*a(n-1) - 75*a(n-2) + 145*a(n-3) - 120*a(n-4) + 36*a(n-5) for n>5. %F A151603 (End) %o A151603 (Magma) [0] cat [n*((5/2)*6^n - 25*n) : n in [2..30]]; // _Wesley Ivan Hurt_, Jul 17 2020 %o A151603 (PARI) a(n) = if(n <= 1, 0, n*(5*6^n/2 - 25*n)) \\ _Andrew Howroyd_, May 04 2020 %o A151603 (PARI) Vec(5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2) + O(x^21)) \\ _Colin Barker_, Jul 17 2020 %Y A151603 Cf. A151583. %K A151603 nonn,easy %O A151603 1,2 %A A151603 _R. H. Hardin_, May 21 2009 %E A151603 Terms a(7) and beyond from _Andrew Howroyd_, May 04 2020