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 A120580 #20 Jul 16 2024 15:56:02
%S A120580 1,0,-4,-8,0,32,64,0,-256,-512,0,2048,4096,0,-16384,-32768,0,131072,
%T A120580 262144,0,-1048576,-2097152,0,8388608,16777216,0,-67108864,-134217728,
%U A120580 0,536870912,1073741824,0,-4294967296,-8589934592,0,34359738368,68719476736,0,-274877906944,-549755813888,0
%N A120580 Hankel transform of Sum_{k=0..n} C(2k,k).
%C A120580 Hankel transform of A006134.
%C A120580 Hankel transform of A098479. - _Paul Barry_, Sep 19 2008
%C A120580 Hankel transform of A025565. - _Paul Barry_, Mar 26 2010
%H A120580 Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Barry/barry321.html">Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices</a>, Journal of Integer Sequences, 19, 2016, #16.3.5.
%H A120580 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-4).
%F A120580 G.f.: (1-2x)/(1-2x+4x^2).
%F A120580 a(n) = 2^n*(cos(Pi*n/3)-sin(Pi*n/3)/sqrt(3)).
%F A120580 E.g.f.: exp(x)*(cos(sqrt(3)*x) - sin(sqrt(3)*x)/sqrt(3)). - _Stefano Spezia_, Jul 15 2024
%t A120580 LinearRecurrence[{2,-4},{1,0},50] (* _Harvey P. Dale_, Feb 13 2023 *)
%Y A120580 Cf. A006134, A025565, A098479, A104538.
%K A120580 easy,sign
%O A120580 0,3
%A A120580 _Paul Barry_, Jun 15 2006