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A192128 Number of set partitions of {1, ..., n} that avoid 7-nestings 0


%S 1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,

%T 190899321,1382958475,10480139391,82864788832,682074818390,

%U 5832698911490

%N Number of set partitions of {1, ..., n} that avoid 7-nestings

%C This is equal to the number of set partitions of {1, ..., n} that avoid 7-crossings.

%C 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]

%H M. Bousquet-Mélou and G. Xin, <a href="https://arxiv.org/abs/math/0506551">On partitions avoiding 3-crossings</a>, arXiv:math/0506551 [math.CO], 2005-2006.

%H Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, <a href="http://arxiv.org/abs/1108.5615">A generating tree approach to k-nonnesting partitions and permutations</a>, arXiv preprint arXiv:1108.5615 [math.CO], 2011.

%H W. Chen, E. Deng, R. Du, R. Stanley, and C. Yan, <a href="https://arxiv.org/abs/math/0501230">Crossings and nestings of matchings and partitions</a>, arXiv:math/0501230 [math.CO], 2005.

%H M. Mishna and L. Yen, <a href="http://arxiv.org/abs/1106.5036">Set partitions with no k-nesting</a>, arXiv:1106.5036 [math.CO], 2011-2012.

%e 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.

%Y Cf. A000110.

%K nonn,more

%O 0,3

%A _Marni Mishna_, Jun 23 2011

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Last modified June 23 18:45 EDT 2021. Contains 345402 sequences. (Running on oeis4.)