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%I #13 Apr 24 2016 22:27:37
%S 1,0,2,-6,30,-150,806,-4494,25822,-151782,908502,-5518590,33933774,
%T -210814422,1321230150,-8343458286,53037407166,-339111023046,
%U 2179407749558,-14071216784862,91225811704750,-593639364476598
%N Expansion of (3(1-x)-sqrt(1+6x-7x^2))/(2(1-x)(1-2x)).
%C First column of inverse of Riordan array ((1+x)/(1+x+2x^2),x(1+2x)/(1+x+2x^2)).
%C Hankel transform is A002416. Binomial transform of A114191.
%D A. Hora, N. Obata, Quantum Probability and Spectral Analysis of Graphs, Springer, 2007, p. 122
%H G. C. Greubel, <a href="/A166078/b166078.txt">Table of n, a(n) for n = 0..500</a>
%F G.f.: 1/(1-x+x*c(-2x/(1-x))), c(x) the g.f. of A000108.
%F G.f.: 1/(1-2x^2/(1-3x-4x^2/(1-3x-4x^2/(1-3x-4x^2/(1-... (continued fraction).
%F Conjecture: n*a(n) + 2*(2*n-5)*a(n-1) + (34-19*n)*a(n-2) + 14*(n-2)*a(n-3)=0. - _R. J. Mathar_, Nov 14 2011
%t CoefficientList[Series[(3 (1 - x) - Sqrt[1 + 6 x - 7 x^2])/(2 (1 - x) (1 - 2 x)), {x, 0, 50}], x](* _G. C. Greubel_, Apr 24 2016 *)
%K easy,sign
%O 0,3
%A _Paul Barry_, Oct 06 2009
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