A192866 Number of set partitions of {1, ..., n} that avoid enhanced 6-crossings (or enhanced 6-nestings).

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213555, 27643388, 190878823, 1382610179, 10474709625, 82784673008, 680933897225, 5816811952612, 51505026270176

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

Example

There are 678570 partitions of 11 elements, but a(11)=678569 because the partition {1,11}{2,10}{3,9}{4,8}{5,9}{6} has an enhanced 6-nesting.

Crossrefs

Cf. A000110, A108307, A192855, A192865.

Sequence in context: A287671 A164864 A366776 * A229227 A287589 A287282

Adjacent sequences: A192863 A192864 A192865 * A192867 A192868 A192869

Keyword

nonn

Author

Marni Mishna, Jul 11 2011

Status

approved