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 A104721 #19 Sep 08 2022 08:45:17
%S A104721 1,2,5,8,20,32,80,128,320,512,1280,2048,5120,8192,20480,32768,81920,
%T A104721 131072,327680,524288,1310720,2097152,5242880,8388608,20971520,
%U A104721 33554432,83886080,134217728,335544320,536870912,1342177280,2147483648
%N A104721 Expansion of (1+x)^2/(1-4*x^2).
%C A104721 Binomial transform is A033113.
%C A104721 Let b(n) = binomial(n-1, (n-1)/2)*(1-(-1)^n)/2 + binomial(n, n/2)*(1+(-1)^n)/2. Then a(n) = Sum_{k=0..n} b(k)*b(n-k).
%C A104721 If a(1)=2 is dropped, sequence becomes identical to A084568 (Proof immediate by standard manipulation of the two generating functions). - _R. J. Mathar_, May 19 2008
%H A104721 G. C. Greubel, <a href="/A104721/b104721.txt">Table of n, a(n) for n = 0..1000</a>
%H A104721 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4).
%F A104721 a(n) = (9*2^n + (-2)^n - 2*0^n)/8.
%t A104721 CoefficientList[Series[(1+x)^2/(1-4x^2),{x,0,40}],x] (* or *) LinearRecurrence[{0,4},{1,2,5},40] (* _Harvey P. Dale_, Dec 05 2015 *)
%o A104721 (PARI) vector(40, n, n--; (9*2^n +(-2)^n -2*0^n)/8) \\ _G. C. Greubel_, Jul 14 2019
%o A104721 (Magma) [1] cat [9*2^(n-3) -(-2)^(n-3): n in [1..40]]; // _G. C. Greubel_, Jul 14 2019
%o A104721 (Sage) [1]+[9*2^(n-3) -(-2)^(n-3) for n in (1..40)] # _G. C. Greubel_, Jul 14 2019
%o A104721 (GAP) Concatenation([1], List([1..40], n-> 9*2^(n-3) -(-2)^(n-3))); # _G. C. Greubel_, Jul 14 2019
%K A104721 easy,nonn
%O A104721 0,2
%A A104721 _Paul Barry_, Mar 20 2005