

A074922


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


2



0, 0, 0, 3, 28, 180, 990, 5005, 24024, 111384, 503880, 2238390, 9806280, 42493880, 182530530, 778439025, 3300049200, 13919756400, 58462976880, 244639718730, 1020422356200, 4244365452600, 17610393500700, 72907029092898
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..23.
V. Pilaud, J. RuĂ©, Analytic combinatorics of chord and hyperchord diagrams with k crossings, arXiv preprint arXiv:1307.6440, 2013
H. Bottomley, Illustration for A000108, A001147, A002694, A067310 and A067311


FORMULA

a(n) = C(2n, n2)*(n2)/2 = A002694(n)*(n2)/2 = A067310(n, 2) = Sum_{0<=j<n} (1)^j*C((nj)*(nj+1)/212, n1)*(C(2n, j)C(2n, j1)).


EXAMPLE

a(3)=3 since the only possibility is to have one of the three chords intersected by the other two.


MATHEMATICA

Table[Binomial[2n, n2] (n2)/2, {n, 0, 30}] (* Harvey P. Dale, Nov 04 2011 *)


CROSSREFS

Cf. A067310, A002694, A232224, A274404.
Sequence in context: A012778 A302522 A303405 * A285365 A160872 A081019
Adjacent sequences: A074919 A074920 A074921 * A074923 A074924 A074925


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Oct 06 2002


STATUS

approved



