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%I #12 May 17 2013 03:32:57
%S 0,1,0,3,2,9,6,29,30,99,112,351,450,1275,1734,4707,6762,17577,26208,
%T 66197,101862,250953,395804,956385,1540110,3660541,5997600,14061141,
%U 23382294,54177741,91246662,209295261,356432166,810375651,1393592512
%N Number of rational knots of n crossings with signature 0 (chiral pairs counted twice).
%H Vincenzo Librandi, <a href="/A078478/b078478.txt">Table of n, a(n) for n = 3..1000</a>
%H A. Stoimenow, <a href="http://arXiv.org/abs/math.GT/0210174">Generating Functions, Fibonacci Numbers and Rational Knots</a>
%F G.f.: (-x/2)*( 2 + (2*x^4-x^2-1)/(sqrt(1-4*x^4)*(1+x^2)) + (2*x^2-x-1)/(sqrt(1-4*x^2)*(1+x)) ) - Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 01 2006
%F a(2n+4) = A006134(n-1) = Sum[ (2k)!/(k!)^2, {k,0,n} ]. - _Alexander Adamchuk_, Feb 23 2007
%t CoefficientList[Series[(- x/2) (2 + (2*x^4 - x^2 - 1) / (Sqrt[1 - 4 x^4] (1 + x^2)) + (2 x^2 - x - 1) / (Sqrt[1 - 4 x^2] (1 + x))) / x^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 17 2013 *)
%Y Cf. A006134.
%K nonn
%O 3,4
%A _Ralf Stephan_, Jan 03 2003
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 01 2006
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