A192126 Number of set partitions of {1, ..., n} that avoid 5-nestings.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678530, 4212654, 27627153, 190624976, 1378972826, 10425400681, 82139435907, 672674215928, 5712423473216, 50193986895328, 455436027242590, 4259359394306331

Offset

0,3

Comments

a(n) is also equal to the number of set partitions of {1, ..., n} that avoid 5-crossings.

Links

Table of n, a(n) for n=0..22.

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

Cf. A108304, A108305.

Sequence in context: A287258 A287670 A164863 * A229226 A343671 A276726

Adjacent sequences: A192123 A192124 A192125 * A192127 A192128 A192129

Keyword

nonn,more

Author

Marni Mishna, Jun 23 2011

Status

approved