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A232224
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Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 3 simple intersections.
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3
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0, 0, 0, 1, 20, 195, 1430, 9009, 51688, 278460, 1434120, 7141530, 34648856, 164663785, 769491450, 3546222225, 16152872400, 72846725160, 325722299760, 1445598337950, 6373942543800, 27942072562950, 121863923024844, 529043313674106, 2287209524819120
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OFFSET
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0,5
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LINKS
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FORMULA
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Pilaud-Rue give an explicit g.f.
a(n) = [x^(2n)] (1-sqrt(1-4*x^2))^6*((1-x^2)*sqrt(1-4*x^2)+7*x^2-26*x^4) / (64*x^6*sqrt(1-4*x^2)^5). - Michel Marcus, Sep 30 2015
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MATHEMATICA
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CoefficientList[Series[(1 - Sqrt[1 - 4 x^2])^6 ((1 - x^2) Sqrt[1 - 4 x^2] + 7 x^2 - 26 x^4)/(64 x^6 Sqrt[1 - 4 x^2]^5), {x, 0, 48}], x^2] (* Michael De Vlieger, Sep 30 2015 *)
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PROG
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(PARI) lista(nn) = {np = 2*nn+2; default(seriesprecision, np); pol = (1-sqrt(1-4*x^2))^6*((1-x^2)*sqrt(1-4*x^2)+7*x^2-26*x^4)/(64*x^6*sqrt(1-4*x^2)^5) + O(x^(np)); forstep (n=0, 2*nn, 2, print1(polcoeff(pol, n), ", "); ); } \\ Michel Marcus, Sep 30 2015
(PARI) x='x+O('x^33); concat([0, 0, 0], Vec((1-sqrt(1-4*x))^6*((1-x)*sqrt(1-4*x)+7*x-26*x^2) / (64*x^3*sqrt(1-4*x)^5))) \\ Joerg Arndt, Sep 30 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Corrected initial terms and more terms from Lars Blomberg, Sep 30 2015
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STATUS
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approved
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