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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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2
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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
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OFFSET
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0,4
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LINKS
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FORMULA
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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
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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
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Table[Binomial[2n, n-2] (n-2)/2, {n, 0, 30}] (* Harvey P. Dale, Nov 04 2011 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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