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%I #19 Jan 30 2020 21:29:18
%S 1,0,0,-1,-6,-30,-142,-660,-3054,-14154,-65886,-308442,-1452940,
%T -6887508,-32852082,-157630609,-760599954,-3689418510,-17984138984,
%U -88063955880,-433048404780,-2137792856760,-10591472304270,-52648861274730,-262514740621860,-1312653157205088,-6580914381986160
%N G.f.: 2C(x)/(3-sqrt(1-4xC(x))) where C = g.f. for A000108.
%H Vincenzo Librandi, <a href="/A285195/b285195.txt">Table of n, a(n) for n = 0..1000</a>
%H Tian-Xiao He, Louis W. Shapiro, <a href="https://doi.org/10.1016/j.laa.2016.05.035">Row sums and alternating sums of Riordan arrays</a>, Linear Algebra and its Applications, Volume 507, 15 October 2016, Pages 77-95. See R_3^{-}.
%F G.f.: 2*(1-sqrt(1-4*x))/(2*x)/(3-sqrt(1-4*x*(1-sqrt(1-4*x))/(2*x))). - _Vincenzo Librandi_, Apr 29 2017
%F Conjecture D-finite with recurrence: +126*n*(n-1)*(n+1)*a(n) -3*n*(n-1)*(691*n-1037)*a(n-1) +(n-1)*(12023*n^2-48049*n+47736)*a(n-2) +2*(-12889*n^3+93970*n^2-221427*n+169506)*a(n-3) +4*(-248*n^3+12718*n^2-88433*n+160113)*a(n-4) +16*(2918*n^3-41574*n^2+198532*n-317121)*a(n-5) +240*(4*n-19)*(2*n-9)*(4*n-21)*a(n-6)=0. - _R. J. Mathar_, Jan 25 2020
%t CoefficientList[Series[2 (1 - Sqrt[1 - 4 x]) / (2 x) / (3 - Sqrt[1 - 4 x (1 - Sqrt[1 - 4 x]) / (2 x)]), {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 29 2017 *)
%K sign
%O 0,5
%A _N. J. A. Sloane_, Apr 28 2017
%E More terms from _Ilya Gutkovskiy_, Apr 28 2017
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