cp's OEIS Frontend

A232224 Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 3 simple intersections.

%I A232224 #25 Jun 20 2016 11:44:20
%S A232224 0,0,0,1,20,195,1430,9009,51688,278460,1434120,7141530,34648856,
%T A232224 164663785,769491450,3546222225,16152872400,72846725160,325722299760,
%U A232224 1445598337950,6373942543800,27942072562950,121863923024844,529043313674106,2287209524819120
%N A232224 Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 3 simple intersections.
%H A232224 Lars Blomberg, <a href="/A232224/b232224.txt">Table of n, a(n) for n = 0..100</a>
%H A232224 V. Pilaud, J. Rué, <a href="http://arxiv.org/abs/1307.6440">Analytic combinatorics of chord and hyperchord diagrams with k crossings</a>, arXiv preprint arXiv:1307.6440 [math.CO], 2013.
%F A232224 Pilaud-Rue give an explicit g.f.
%F A232224 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
%t A232224 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 *)
%o A232224 (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
%o A232224 (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
%Y A232224 Cf. A002694, A074922, A274404.
%K A232224 nonn
%O A232224 0,5
%A A232224 _N. J. A. Sloane_, Nov 22 2013
%E A232224 Corrected initial terms and more terms from _Lars Blomberg_, Sep 30 2015