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A078478
Number of rational knots of n crossings with signature 0 (chiral pairs counted twice).
5
0, 1, 0, 3, 2, 9, 6, 29, 30, 99, 112, 351, 450, 1275, 1734, 4707, 6762, 17577, 26208, 66197, 101862, 250953, 395804, 956385, 1540110, 3660541, 5997600, 14061141, 23382294, 54177741, 91246662, 209295261, 356432166, 810375651, 1393592512
OFFSET
3,4
FORMULA
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
a(2n+4) = A006134(n-1) = Sum[ (2k)!/(k!)^2, {k,0,n} ]. - Alexander Adamchuk, Feb 23 2007
MATHEMATICA
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 *)
CROSSREFS
Cf. A006134.
Sequence in context: A082819 A298733 A197311 * A346109 A362220 A019778
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jan 03 2003
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 01 2006
STATUS
approved