OFFSET
0,3
COMMENTS
a(n) is also equal to the number of set partitions of {1, ..., n} that avoid 5-crossings.
LINKS
M. Bousquet-Mélou and G. Xin, On partitions avoiding 3-crossings, arXiv:math/0506551 [math.CO], 2005-2006.
Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, A generating tree approach to k-nonnesting partitions and permutations, arXiv preprint arXiv:1108.5615 [math.CO], 2011.
W. Chen, E. Deng, R. Du, R. Stanley, and C. Yan, Crossings and nestings of matchings and partitions, arXiv:math/0501230 [math.CO], 2005.
Juan B. Gil and Jordan O. Tirrell, A simple bijection for classical and enhanced k-noncrossing partitions, arXiv:1806.09065 [math.CO], 2018. Also Discrete Mathematics (2019) Article 111705. doi:10.1016/j.disc.2019.111705
M. Mishna and L. Yen, Set partitions with no k-nesting, arXiv:1106.5036 [math.CO], 2011-2012.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Marni Mishna, Jun 23 2011
STATUS
approved