A192855 Number of set partitions of {1, ..., n} that avoid enhanced 4-crossings (or enhanced 4-nestings)

1, 1, 2, 5, 15, 52, 203, 876, 4120, 20883, 113034, 648410, 3917021, 24785452, 163525976, 1120523114, 7947399981, 58172358642, 438300848329, 3391585460591, 26898763482122

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 877 partitions of 7 elements, but a(7)=51 because the partition {1,7}{2,6}{3,5}{4} has an enhanced 4-nesting.

Crossrefs

Cf. A000110, A108307.

Sequence in context: A141080 A366774 A287667 * A148092 A343667 A276723

Adjacent sequences: A192852 A192853 A192854 * A192856 A192857 A192858

Keyword

nonn

Author

Marni Mishna, Jul 11 2011

Status

approved