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Number of set partitions of {1, ..., n} that avoid enhanced 6-crossings (or enhanced 6-nestings).
1

%I #16 Dec 04 2016 11:08:35

%S 1,1,2,5,15,52,203,877,4140,21147,115975,678569,4213555,27643388,

%T 190878823,1382610179,10474709625,82784673008,680933897225,

%U 5816811952612,51505026270176

%N Number of set partitions of {1, ..., n} that avoid enhanced 6-crossings (or enhanced 6-nestings).

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

%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, 2011

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

%e There are 678570 partitions of 11 elements, but a(11)=678569 because the partition {1,11}{2,10}{3,9}{4,8}{5,9}{6} has an enhanced 6-nesting.

%Y Cf. A000110, A108307, A192855, A192865.

%K nonn

%O 0,3

%A _Marni Mishna_, Jul 11 2011