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 A188589 #15 Oct 20 2024 00:27:46
%S A188589 1,1,5,14,33,72,151,310,629,1268,2547,5106,10225,20464,40943,81902,
%T A188589 163821,327660,655339,1310698,2621417,5242856,10485735,20971494,
%U A188589 41943013,83886052,167772131,335544290,671088609,1342177248,2684354527
%N A188589 Expansion of (1-3*x+6*x^2-3*x^3)/((1-x)^2*(1-2*x)).
%C A188589 Second column of the 1-Euler triangle A188587. In general, the second column of the r-Euler triangle has g.f. (1-(4-r)*x+2*(4-r)*x^2-(4-r)*x^3)/((1-x)^2*(1-2*x)).
%H A188589 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A188589 a(n+1)=A094002(n).
%F A188589 a(n) = 5*2^(n-1)-n-3, n>0.
%t A188589 CoefficientList[Series[(1-3x+6x^2-3x^3)/((1-x)^2(1-2x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,-5,2},{1,1,5,14},40] (* _Harvey P. Dale_, Nov 26 2017 *)
%o A188589 (PARI) a(n) = if (n==0, 1, 5*2^(n-1) - n - 3) \\ _Michel Marcus_, Jul 24 2013
%K A188589 nonn,easy
%O A188589 0,3
%A A188589 _Paul Barry_, Apr 04 2011