%I
%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 7nestings
%C This is equal to the number of set partitions of {1, ..., n} that avoid 7crossings.
%C The first 14 terms coincide with terms of A000110. Without avoidance of 7crossings, the two sequences would be identical. [_Alexander R. Povolotsky_, Sep 19 2011]
%H M. BousquetMÃ©lou and G. Xin, <a href="https://arxiv.org/abs/math/0506551">On partitions avoiding 3crossings</a>, arXiv:math/0506551 [math.CO], 20052006.
%H Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, <a href="http://arxiv.org/abs/1108.5615">A generating tree approach to knonnesting 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 knesting</a>, arXiv:1106.5036 [math.CO], 20112012.
%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 7nesting.
%Y Cf. A000110.
%K nonn,more
%O 0,3
%A _Marni Mishna_, Jun 23 2011
