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Search: id:A108304
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| A108304 |
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Number of set partitions of {1, ..., n} that avoid 3-crossings. |
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+0
1
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| 1, 1, 2, 5, 15, 52, 202, 859, 3930, 19095, 97566, 520257, 2877834, 16434105, 96505490, 580864901, 3573876308, 22426075431, 143242527870, 929759705415, 6123822269373
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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There is also a sum-formula for a(n). See Bousquet-Melou and Xin.
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LINKS
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M. Bousquet-Melou and G. Xin, On partitions avoiding 3-crossings, math.CO/0506551.
Chen, W., Deng, E., Du, R., Stanley, R. and Yan, C., Crossings and nestings of matchings and partitions, math.CO/0501230
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FORMULA
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(9*n^2+27*n)*a(n)+(-10*n^2-64*n-84)*a(n+1)+(n^2+13*n+42)*a(n+2)=0
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EXAMPLE
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There are 203 partitions of 6 elements, but a(6)=202 because the partition (1,4)(2,5)(3,6) has a 3-crossing
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CROSSREFS
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Sequence in context: A007312 A007296 A056272 this_sequence A056273 A099262 A108305
Adjacent sequences: A108301 A108302 A108303 this_sequence A108305 A108306 A108307
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KEYWORD
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easy,nonn
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AUTHOR
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Mireille Bousquet-Melou (bousquet(AT)labri.fr), Jun 29 2005
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