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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..23.

V. Pilaud, J. Rué, 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, 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)).

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, n-2] (n-2)/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

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Last modified November 28 20:27 EST 2020. Contains 338755 sequences. (Running on oeis4.)