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%I #14 Feb 13 2023 16:02:41
%S 1,0,-4,-8,0,32,64,0,-256,-512,0,2048,4096,0,-16384,-32768,0,131072,
%T 262144,0,-1048576,-2097152,0,8388608,16777216,0,-67108864,-134217728,
%U 0,536870912,1073741824,0,-4294967296,-8589934592,0,34359738368,68719476736,0,-274877906944,-549755813888,0
%N Hankel transform of sum{k=0..n, C(2k,k)}.
%C Hankel transform of A006134.
%C Hankel transform of A098479. [_Paul Barry_, Sep 19 2008]
%C Hankel transform of A025565. [_Paul Barry_, Mar 26 2010]
%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-4).
%F G.f.: (1-2x)/(1-2x+4x^2).
%F a(n) = 2^n*(cos(Pi*n/3)-sin(Pi*n/3)/sqrt(3)).
%t LinearRecurrence[{2,-4},{1,0},50] (* _Harvey P. Dale_, Feb 13 2023 *)
%Y Cf. A104538.
%K easy,sign
%O 0,3
%A _Paul Barry_, Jun 15 2006
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