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

%I

%S 1,1,2,4,6,6,3,1,10,34,45,-21,-173,-181,406,1488,1050,-4198,-11931,

%T -3989,43513,97305,-8008,-438126,-781169,468631,4335188,6065206,

%U -7930890,-42174786,-44121989,106840385,402942250,281085066,-1301476803

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

%H Vincenzo Librandi, <a href="/A134920/b134920.txt">Table of n, a(n) for n = 0..200</a>

%F 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.

%F 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

%F Lim sup n->infinity |a(n)|^(1/n) = sqrt(5). - _Vaclav Kotesovec_, Feb 01 2014

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

%Y Cf. A134389.

%K easy,sign

%O 0,3

%A _Paul Barry_, Nov 14 2007

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Last modified August 1 18:47 EDT 2021. Contains 346402 sequences. (Running on oeis4.)