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 A123344 #37 Sep 08 2022 08:45:28
%S A123344 1,1,-2,4,-8,16,-32,64,-128,256,-512,1024,-2048,4096,-8192,16384,
%T A123344 -32768,65536,-131072,262144,-524288,1048576,-2097152,4194304,
%U A123344 -8388608,16777216,-33554432,67108864,-134217728,268435456,-536870912,1073741824,-2147483648
%N A123344 Expansion of (1+3*x)/(1+2*x).
%C A123344 Inverse binomial transform of A000034.
%C A123344 Hankel transform is [1,-3,0,0,0,0,0,0,0,0,...].
%H A123344 G. C. Greubel, <a href="/A123344/b123344.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..200 from Vincenzo Librandi)
%H A123344 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-2).
%F A123344 a(0)=1, a(n) = (-2)^(n-1) for n>0.
%F A123344 G.f.: (1+3*x)/(1+2*x).
%F A123344 G.f.: 1/U(0) where U(k)= 1 - x*(k+4) + x*(k+3)/U(k+1); (continued fraction, 1-step). - _Sergei N. Gladkovskii_, Oct 11 2012
%F A123344 E.g.f.: (3 - exp(-2*x))/2. - _G. C. Greubel_, Oct 12 2017
%F A123344 a(n) = numerator((1/2 - n)!/sqrt(Pi)). - _Peter Luschny_, Jun 21 2020
%p A123344 a:=n->mul(-2, k=0..n): seq(a(n), n=-2..30); # _Zerinvary Lajos_, Jan 22 2008
%t A123344 Table[(-2)^(n - Sign[n]), {n, 0, 30}] (* _Wesley Ivan Hurt_, Feb 01 2014 *)
%t A123344 Join[{1},LinearRecurrence[{-2},{1},32]] (* _Ray Chandler_, Aug 12 2015 *)
%t A123344 Join[{1},NestList[-2#&,1,40]] (* _Harvey P. Dale_, Aug 24 2019 *)
%o A123344 (Magma) [1] cat [(-2)^(n-1): n in [1..35]]; // _Vincenzo Librandi_, Feb 14 2014
%o A123344 (PARI) x='x+O('x^50); Vec((1+3*x)/(1+2*x)) \\ _G. C. Greubel_, Oct 12 2017
%Y A123344 Cf. A011782 (unsigned version).
%K A123344 easy,sign
%O A123344 0,3
%A A123344 _Philippe Deléham_, Oct 11 2006