A074922 Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 2 simple intersections.
0, 0, 0, 3, 28, 180, 990, 5005, 24024, 111384, 503880, 2238390, 9806280, 42493880, 182530530, 778439025, 3300049200, 13919756400, 58462976880, 244639718730, 1020422356200, 4244365452600, 17610393500700, 72907029092898
Offset: 0
Examples
a(3)=3 since the only possibility is to have one of the three chords intersected by the other two.
Links
- Anwar Al Ghabra, K. Gopala Krishna, Patrick Labelle, and Vasilisa Shramchenko, Enumeration of multi-rooted plane trees, arXiv:2301.09765 [math.CO], 2023.
- Vincent Pilaud and Juanjo Rué, Analytic combinatorics of chord and hyperchord diagrams with k crossings, arXiv preprint arXiv:1307.6440, 2013
- Henry Bottomley, Illustration for A000108, A001147, A002694, A067310 and A067311
- N. J. Wildberger and Dean Rubine, A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode, Amer. Math. Monthly (2025). See section 12.
Programs
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Mathematica
Table[Binomial[2n,n-2] (n-2)/2,{n,0,30}] (* Harvey P. Dale, Nov 04 2011 *)