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%I #20 Jan 28 2023 15:46:41
%S 0,0,0,3,28,180,990,5005,24024,111384,503880,2238390,9806280,42493880,
%T 182530530,778439025,3300049200,13919756400,58462976880,244639718730,
%U 1020422356200,4244365452600,17610393500700,72907029092898
%N Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 2 simple intersections.
%H Anwar Al Ghabra, K. Gopala Krishna, Patrick Labelle, and Vasilisa Shramchenko, <a href="https://arxiv.org/abs/2301.09765">Enumeration of multi-rooted plane trees</a>, arXiv:2301.09765 [math.CO], 2023.
%H Vincent Pilaud and Juanjo 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, 2013
%H Henry Bottomley, <a href="/A002694/a002694.gif">Illustration for A000108, A001147, A002694, A067310 and A067311</a>
%F a(n) = C(2n, n-2)*(n-2)/2 = A002694(n)*(n-2)/2 = A067310(n, 2) = Sum_{0<=j<n} (-1)^j*C((n-j)*(n-j+1)/2-1-2, n-1)*(C(2n, j)-C(2n, j-1)).
%e a(3)=3 since the only possibility is to have one of the three chords intersected by the other two.
%t Table[Binomial[2n,n-2] (n-2)/2,{n,0,30}] (* _Harvey P. Dale_, Nov 04 2011 *)
%Y Cf. A067310, A002694, A232224, A274404.
%K nonn,easy
%O 0,4
%A _Henry Bottomley_, Oct 06 2002
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