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 A055586 #19 Jul 31 2025 11:56:47
%S A055586 1,10,59,268,1037,3598,11535,34832,100369,278546,749587,1966100,
%T A055586 5046293,12714006,31522839,77070360,186122265,444596250,1051721755,
%U A055586 2466250780,5737807901,13254000670,30417092639,69390565408
%N A055586 Sixth column of triangle A055584.
%H A055586 A. F. Y. Zhao, <a href="http://www.emis.de/journals/JIS/VOL17/Zhao/zhao3.html">Pattern Popularity in Multiply Restricted Permutations</a>, Journal of Integer Sequences, 17 (2014), #14.10.3.
%H A055586 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-41,88,-104,64,-16).
%F A055586 G.f.: 1/(((1-x)^2)*(1-2*x)^4).
%F A055586 a(n) = A055584(n+5, 5).
%F A055586 a(n) = Sum_{j=0..n-1} a(j) + A055582(n) for n >= 1.
%F A055586 E.g.f.: exp(x)*(x + 9) + 8*exp(2*x)*(2*x^3 + 3*x^2 + 6*x - 3)/3. - _Stefano Spezia_, Sep 24 2024
%t A055586 CoefficientList[Series[1/(((1-x)^2)(1-2x)^4),{x,0,30}],x] (* or *) LinearRecurrence[{10,-41,88,-104,64,-16},{1,10,59,268,1037,3598},30] (* _Harvey P. Dale_, Jul 31 2025 *)
%o A055586 (PARI) Vec(1/(((1-x)^2)*(1-2*x)^4) + O(x^40)) \\ _Michel Marcus_, Dec 11 2015
%Y A055586 Cf. A055584.
%Y A055586 Partial sums of A027608.
%K A055586 easy,nonn
%O A055586 0,2
%A A055586 _Wolfdieter Lang_, May 26 2000