%I #23 Dec 04 2016 10:44:33
%S 1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213596,27644383,
%T 190897649,1382919174,10479355676,82850735298,681840170501,
%U 5828967784989,51665915664913,473990899143781,4493642492511044,43959218211619150
%N Number of set partitions of {1, ..., n} that avoid 6-nestings.
%C This is equal to the number of set partitions of {1, ..., n} that avoid 6-crossings.
%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 4213597 partitions of 12 elements, but a(12)=4213597 because the partition {1,12}{2,11}{3,10}{4,9}{5,8}{6,7} has a 6-nesting.
%Y Cf. A108304, A108305, A192126.
%K nonn
%O 0,3
%A _Marni Mishna_, Jun 23 2011