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 A151656 #10 Jul 18 2020 10:05:26 %S A151656 0,441,35623,1561238,59287158,2165511047,78259307721,2820153607740, %T A151656 101551366735840,3656082204395957,131621033827371963, %U A151656 4738375497166097906,170581677602043334746,6140941779058210902771,221073915991189916489149,7958661078139728516094136 %N A151656 Number of permutations of 7 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order. %H A151656 Andrew Howroyd, <a href="/A151656/b151656.txt">Table of n, a(n) for n = 1..500</a> %H A151656 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (55,-799,4381,-8884,7552,-2304). %F A151656 a(n) = 36^n - (7*n + 1)*8^n + 7*n*(7*n + 1)/2. - _Andrew Howroyd_, May 06 2020 %F A151656 From _Colin Barker_, Jul 18 2020: (Start) %F A151656 G.f.: 49*x^2*(9 + 232*x - 932*x^2 - 1024*x^3) / ((1 - x)^3*(1 - 8*x)^2*(1 - 36*x)). %F A151656 a(n) = 55*a(n-1) - 799*a(n-2) + 4381*a(n-3) - 8884*a(n-4) + 7552*a(n-5) - 2304*a(n-6) for n>6. %F A151656 (End) %o A151656 (PARI) a(n) = {36^n - (7*n + 1)*8^n + 7*n*(7*n + 1)/2} \\ _Andrew Howroyd_, May 06 2020 %o A151656 (PARI) concat(0, Vec(49*x^2*(9 + 232*x - 932*x^2 - 1024*x^3) / ((1 - x)^3*(1 - 8*x)^2*(1 - 36*x)) + O(x^40))) \\ _Colin Barker_, Jul 18 2020 %Y A151656 Cf. A151624. %K A151656 nonn,easy %O A151656 1,2 %A A151656 _R. H. Hardin_, May 29 2009 %E A151656 Terms a(7) and beyond from _Andrew Howroyd_, May 06 2020