A166078 - OEIS

%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