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 A119306 #12 Mar 02 2017 21:07:04
%S A119306 1,-3,-6,6,14,-19,-37,56,96,-164,-247,477,630,-1378,-1590,3957,3963,
%T A119306 -11300,-9728,32104,23425,-90771,-55006,255478,124758,-715923,-268757,
%U A119306 1997808,531552,-5552220,-884695,15368813,834686,-42373618,2113458,116369557,-17926357
%N A119306 Expansion of (1-4*x)/(1-x*(1-x)^3).
%C A119306 Row sums of number triangle A119305.
%H A119306 Indranil Ghosh, <a href="/A119306/b119306.txt">Table of n, a(n) for n = 0..4534</a>
%H A119306 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-3,3,-1).
%F A119306 G.f.: (1 - 4*x)/(1 - x + 3*x^2 - 3*x^3 + x^4).
%F A119306 a(n) = a(n-1) - 3*a(n-2) + 3*a(n-3) - a(n-4).
%F A119306 a(n) = Sum_{k=0..n} (C(3*k,n-k) + 4*C(3*k,n-k-1))*(-1)^(n-k).
%t A119306 CoefficientList[Series[(1 - 4 x)/(1 - x (1 - x)^3), {x, 0, 36}], x] (* or *) LinearRecurrence[{1, -3, 3, -1}, {1, -3, -6, 6}, 37] (* or *) Table[Sum[(Binomial[3 k, n - k] + 4 Binomial[3 k, n - k - 1]) (-1)^(n - k), {k, 0, n}], {n, 0, 36}] (* _Indranil Ghosh_, Feb 27 2017 *)
%o A119306 (PARI) a(n) = sum(k=0,n,(binomial(3*k,n-k)+4*binomial(3*k,n-k-1))*(-1)^(n-k)); \\ _Indranil Ghosh_, Feb 27 2017
%K A119306 sign,easy
%O A119306 0,2
%A A119306 _Paul Barry_, May 13 2006