A166078 Expansion of (3(1-x)-sqrt(1+6x-7x^2))/(2(1-x)(1-2x)).

1, 0, 2, -6, 30, -150, 806, -4494, 25822, -151782, 908502, -5518590, 33933774, -210814422, 1321230150, -8343458286, 53037407166, -339111023046, 2179407749558, -14071216784862, 91225811704750, -593639364476598

Offset: 0

Author

Paul Barry, Oct 06 2009

Keywords

• easy
• sign

Comments

First column of inverse of Riordan array ((1+x)/(1+x+2x^2),x(1+2x)/(1+x+2x^2)).

Hankel transform is A002416. Binomial transform of A114191.

References

• A. Hora, N. Obata, Quantum Probability and Spectral Analysis of Graphs, Springer, 2007, p. 122

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Programs

Mathematica

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 *)

Formula

G.f.: 1/(1-x+x*c(-2x/(1-x))), c(x) the g.f. of A000108.

G.f.: 1/(1-2x^2/(1-3x-4x^2/(1-3x-4x^2/(1-3x-4x^2/(1-... (continued fraction).

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