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%I #31 Nov 18 2023 06:57:20
%S 1,1,2,5,15,52,203,877,4140,21147,115974,678530,4212654,27627153,
%T 190624976,1378972826,10425400681,82139435907,672674215928,
%U 5712423473216,50193986895328,455436027242590,4259359394306331
%N Number of set partitions of {1, ..., n} that avoid 5-nestings.
%C a(n) is also equal to the number of set partitions of {1, ..., n} that avoid 5-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 Juan B. Gil and Jordan O. Tirrell, <a href="https://arxiv.org/abs/1806.09065">A simple bijection for classical and enhanced k-noncrossing partitions</a>, arXiv:1806.09065 [math.CO], 2018. Also Discrete Mathematics (2019) Article 111705. doi:10.1016/j.disc.2019.111705
%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 115975 partitions of 10 elements, but a(10)=115974 because the partition {1,10}{2,9}{3,8}{4,7}{5,6} has a 5-nesting.
%Y Cf. A108304, A108305.
%K nonn,more
%O 0,3
%A _Marni Mishna_, Jun 23 2011
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