A134920 Expansion of (1-x+sqrt(1-2x+5x^2))/(2(1-x)^2).

1, 1, 2, 4, 6, 6, 3, 1, 10, 34, 45, -21, -173, -181, 406, 1488, 1050, -4198, -11931, -3989, 43513, 97305, -8008, -438126, -781169, 468631, 4335188, 6065206, -7930890, -42174786, -44121989, 106840385, 402942250, 281085066, -1301476803

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

Hankel transform is 1,1,-2,-2,3,3,-4,4,.... Binomial transform of sequence 1,0,1,0,-1,0,2,0,-5,0,14,.... with generating function (1+sqrt(1+4x^2))/2=1+x^2C(-x^2) where C(x) is the g.f. of A000108.

D-finite with recurrence: n*a(n) +(3-4*n)*a(n-1) + (10*n-21)*a(n-2) + (33-12*n)*a(n-3)+ 5*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 14 2011

Lim sup n->infinity |a(n)|^(1/n) = sqrt(5). - Vaclav Kotesovec, Feb 01 2014

Mathematica

CoefficientList[Series[(1-x+Sqrt[1-2*x+5*x^2])/(2*(1-x)^2), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)

Crossrefs

Cf. A134389.

Sequence in context: A010587 A372035 A213473 * A011031 A248844 A257821

Adjacent sequences: A134917 A134918 A134919 * A134921 A134922 A134923

Keyword

easy,sign

Author

Paul Barry, Nov 14 2007

Status

approved