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A074922
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Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 2 simple intersections.
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0
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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; internal format)
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OFFSET
| 0,4
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LINKS
| H. Bottomley, Illustration for A000108, A001147, A002694, A067310 and A067311
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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)).
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EXAMPLE
| a(3)=3 since the only possibility is to have one of the three chords intersected by the other two.
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MATHEMATICA
| Table[Binomial[2n, n-2] (n-2)/2, {n, 0, 30}] (* From Harvey P. Dale, Nov 04 2011 *)
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CROSSREFS
| Cf. A067310.
Sequence in context: A184440 A012762 A012778 * A160872 A081019 A091120
Adjacent sequences: A074919 A074920 A074921 * A074923 A074924 A074925
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 06 2002
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