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Search: id:A108307
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| A108307 |
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Number of set partitions of {1, ..., n} that avoid enhanced 3-crossings (or enhanced 3-nestings). |
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1
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| 1, 1, 2, 5, 15, 51, 191, 772, 3320, 15032, 71084, 348889, 1768483, 9220655, 49286863, 269346822, 1501400222, 8519796094, 49133373040, 287544553912, 1705548000296
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also the number of 2-regular 3-noncrossing partitions. There is a bijection from 2-regular 3-noncrossing partitions of n to enhanced partition of n-1. - Jing Qin (qj(AT)cfc.nankai.edu.cn), Oct 30 2007
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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. P. and Yan, C., Crossings and nestings of matchings and partitions, math.CO/0501230
Emma Y. Jin, Jing Qin and Christian M. Reidys, On 2-regular k-noncrossing partitions, math.CO/07105014.
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FORMULA
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Recurrence: 8*(n+3)*(n+1)*a(n)+(7*n^2+53*n+88)*a(n+1)-(n+8)*(n+7)*a(n+2)=0 - Jing Qin (qj(AT)cfc.nankai.edu.cn), Oct 26 2007
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EXAMPLE
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There are 52 partitions of 5 elements, but a(5)=51 because the partition (1,5)(2,4)(3) has an enhanced 3-nesting
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CROSSREFS
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Cf. A124303 A073525 A007317.
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KEYWORD
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easy,nonn,new
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AUTHOR
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Mireille Bousquet-Melou (bousquet(AT)labri.fr), Jun 29 2005
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EXTENSIONS
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Edited by njas at the suggestion of Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 27 2008
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