%I
%S 1,4,1,8,1,12,1,16,1,20,1,24,1,28,1,32,1,36,1,40,1,44,1,
%T 48,1,52,1,56,1,60,1,64,1,68,1,72,1,76,1,80,1,84,1,88,1,92,
%U 1,96,1,100,1,104,1,108,1,112,1,116,1,120,1,124,1,128,1,132,1
%N Expansion of (14x+x^2)/(1+x^2)^2.
%C Hankel transform of A158495.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 0, 1).
%F a(n) = ((n+3/2(n+1/2)*(1)^n)*(1)^C(n+1,2).
%F a(0)=1, a(1)=4, a(2)=1, a(3)=8, a(n) = 2*a(n2)a(n4). [_Harvey P. Dale_, Mar 06 2012]
%t CoefficientList[Series[(14x+x^2)/(1+x^2)^2,{x,0,70}],x] (* or *) LinearRecurrence[{0,2,0,1},{1,4,1,8},70] (* _Harvey P. Dale_, Mar 06 2012 *)
%o (PARI) Vec((14*x+x^2)/(1+x^2)^2 + O(x^100)) \\ _Altug Alkan_, Jan 10 2016
%Y Cf. A019425.
%K easy,sign
%O 0,2
%A _Paul Barry_, Mar 20 2009
