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 A084633 #21 Mar 19 2023 02:48:26
%S A084633 1,0,2,-4,8,-16,32,-64,128,-256,512,-1024,2048,-4096,8192,-16384,
%T A084633 32768,-65536,131072,-262144,524288,-1048576,2097152,-4194304,8388608,
%U A084633 -16777216,33554432,-67108864,134217728,-268435456,536870912,-1073741824,2147483648,-4294967296
%N A084633 Inverse binomial transform of repeated odd numbers.
%H A084633 G. C. Greubel, <a href="/A084633/b084633.txt">Table of n, a(n) for n = 0..1000</a>
%H A084633 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-2).
%F A084633 a(n) = (0^n + (-2)^n)/2, for n > 1, with a(1) = 0.
%F A084633 abs(a(n)) = A034008(n).
%F A084633 From _Colin Barker_, Jan 06 2013: (Start)
%F A084633 a(n) = (-1)^n * 2^(n-1) for n > 1.
%F A084633 a(n) = -2*a(n-1) for n > 2.
%F A084633 G.f.: (1 +2*x +2*x^2) / (1+2*x). (End)
%F A084633 E.g.f.: (1 + 2*x + exp(-2*x))/2. - _Alejandro J. Becerra Jr._, Jan 29 2021
%t A084633 Join[{1,0}, NestList[-2#&,2,40]] (* _Harvey P. Dale_, Dec 28 2015 *)
%o A084633 (Magma) [n le 1 select 1-n else (0^n + (-2)^n)/2: n in [0..40]]; // _G. C. Greubel_, Mar 18 2023
%o A084633 (SageMath) [(0^n + (-2)^n)/2 + int(n==1) for n in range(41)] # _G. C. Greubel_, Mar 18 2023
%Y A084633 Cf. A034008.
%K A084633 easy,sign
%O A084633 0,3
%A A084633 _Paul Barry_, Jun 05 2003