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A192128
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Number of set partitions of {1, ..., n} that avoid 7-nestings
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0
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1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899321, 1382958475, 10480139391, 82864788832, 682074818390, 5832698911490
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OFFSET
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0,3
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COMMENTS
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This is equal to the number of set partitions of {1, ..., n} that avoid 7-crossings.
The first 14 terms coincide with terms of A000110. Without avoidance of 7-crossings, the two sequences would be identical. [Alexander R. Povolotsky, Sep 19 2011]
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LINKS
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Table of n, a(n) for n=0..19.
M. Bousquet-Mélou and G. Xin, On partitions avoiding 3-crossings, arXiv:math/0506551 [math.CO], 2005-2006.
Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, A generating tree approach to k-nonnesting partitions and permutations, arXiv preprint arXiv:1108.5615 [math.CO], 2011.
W. Chen, E. Deng, R. Du, R. Stanley, and C. Yan, Crossings and nestings of matchings and partitions, arXiv:math/0501230 [math.CO], 2005.
M. Mishna and L. Yen, Set partitions with no k-nesting, arXiv:1106.5036 [math.CO], 2011-2012.
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EXAMPLE
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There are 190899322 partitions of 14 elements, but a(14)=190899321 because the partition {1,14}{2,13}{3,12}{4,11}{5,10}{6,9}{7,8} has a 7-nesting.
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CROSSREFS
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Cf. A000110.
Sequence in context: A203642 A192867 A203643 * A203644 A203645 A203646
Adjacent sequences: A192125 A192126 A192127 * A192129 A192130 A192131
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KEYWORD
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nonn,more
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AUTHOR
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Marni Mishna, Jun 23 2011
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STATUS
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approved
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