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

0,3

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

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

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 *)

Crossrefs

Sequence in context: A055695 A113593 A122763 * A319365 A306946 A319104

Adjacent sequences: A166075 A166076 A166077 * A166079 A166080 A166081

Keyword

easy,sign

Author

Paul Barry, Oct 06 2009

Status

approved