A102882 Expansion of (1+2x)/sqrt((1-3x^2)(1+4x+5x^2)).

1, 0, 1, 2, -3, 16, -27, 66, -79, 96, 129, -686, 2429, -5520, 11125, -15438, 10785, 36032, -182591, 556194, -1279171, 2393296, -3187131, 1157666, 10934481, -48082656, 136730689, -304493326, 539172285, -647406800, -53647147, 3352290450, -12929496767, 34720868736, -74092036479

Offset

0,4

Comments

Binomial transform is A102881.

Links

Table of n, a(n) for n=0..34.

Formula

G.f.: (1+2x)/sqrt(1+4x+2x^2-12x^3-15x^4).

Conjecture: n*(n+1)*a(n) +2*(2*n+3)*(n-1)*a(n-1) +2*(n^2-7)*a(n-2) +6*(5+n-2*n^2)*a(n-3) -15*(n+2)*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 09 2012

Lim sup n->infinity |a(n)|^(1/n) = sqrt(5). - Vaclav Kotesovec, Feb 03 2014

Mathematica

CoefficientList[Series[(1+2*x)/Sqrt[1+4*x+2*x^2-12*x^3-15*x^4], {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 03 2014 *)

Crossrefs

Sequence in context: A074182 A074759 A175699 * A359391 A085734 A302837

Adjacent sequences: A102879 A102880 A102881 * A102883 A102884 A102885

Keyword

easy,sign

Author

Paul Barry, Jan 15 2005

Status

approved