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A192865 Number of set partitions of {1,...,n} that avoid enhanced 5-crossings (or 5-nestings) 2
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115945, 678012, 4205209, 27531954, 189486817, 1365888674, 10278272450, 80503198320, 654544093035, 5511256984436, 47950929125540 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

M. Bousquet-Mélou and G. Xin, On partitions avoiding 3-crossings, math.CO/0506551.

Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, A generating tree approach to k-nonnesting partitions and permutations, arXiv preprint arXiv:1108.5615, 2011

W. Chen, E. Deng, R. Du, R. P. Stanley, and C. Yan, Crossings and nestings of matchings and partitions, math.CO/0501230

Juan B. Gil, 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

EXAMPLE

There are 21147 partitions of 9 elements, but a(9)=21146 because the partition {1,9}{2,8}{3,7}{4, 6}{5} has an enhanced 5-nesting.

CROSSREFS

Cf. A000110, A108307, A192855

Sequence in context: A287257 A287669 A099263 * A229225 A343669 A276725

Adjacent sequences:  A192862 A192863 A192864 * A192866 A192867 A192868

KEYWORD

nonn

AUTHOR

Marni Mishna, Jul 11 2011

STATUS

approved

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Last modified September 18 22:34 EDT 2021. Contains 347548 sequences. (Running on oeis4.)