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 A099570 #12 Jul 25 2022 18:32:00
%S A099570 1,0,0,-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,16,-17,18,-19,20,
%T A099570 -21,22,-23,24,-25,26,-27,28,-29,30,-31,32,-33,34,-35,36,-37,38,-39,
%U A099570 40,-41,42,-43,44,-45,46,-47,48,-49,50,-51,52,-53,54,-55,56,-57,58,-59,60,-61,62,-63,64,-65,66,-67,68,-69,70,-71,72,-73
%N A099570 Expansion of ((1+x)^2 - x^3)/(1+x)^2.
%C A099570 Row sums of number triangle A099569.
%H A099570 G. C. Greubel, <a href="/A099570/b099570.txt">Table of n, a(n) for n = 0..1000</a>
%H A099570 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1).
%F A099570 a(n) = 2*0^n + (-1)^n*(n-2) - Sum_{k=0..n} k*binomial(n, k)*(-1)^(n-k).
%F A099570 a(n) = -2*a(n-1) - a(n-2), n>3, with a(0) = 1, a(1) = 0, a(2) = 0, a(3) = -1.
%F A099570 From _G. C. Greubel_, Jul 25 2022: (Start)
%F A099570 a(n) = (-1)^n*(n-2) - [n=1] + 3*[n=0].
%F A099570 a(n) = A038608(n-2), for n >= 2, with a(0) = 1, a(1) = 0.
%F A099570 E.g.f.: 3 - x - (x+2)*exp(-x). (End)
%t A099570 Table[(-1)^n*(n-2) -Boole[n==1]+3*Boole[n==0], {n,0,100}] (* _G. C. Greubel_, Jul 25 2022 *)
%o A099570 (Magma) [1,0] cat [(-1)^n*(n-2): n in [2..100]]; // _G. C. Greubel_, Jul 25 2022
%o A099570 (SageMath) [(-1)^n*(n-2) -bool(n==1) +3*bool(n==0) for n in (0..100)] # _G. C. Greubel_, Jul 25 2022
%Y A099570 Cf. A038608, A099569.
%K A099570 easy,sign
%O A099570 0,5
%A A099570 _Paul Barry_, Oct 22 2004