|
%I #15 Jan 30 2020 21:29:16
%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
|
