A192127 Number of set partitions of {1, ..., n} that avoid 6-nestings.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213596, 27644383, 190897649, 1382919174, 10479355676, 82850735298, 681840170501, 5828967784989, 51665915664913, 473990899143781, 4493642492511044, 43959218211619150

Offset

0,3

Comments

This is equal to the number of set partitions of {1, ..., n} that avoid 6-crossings.

Links

Table of n, a(n) for n=0..23.

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.

M. Mishna and L. Yen, Set partitions with no k-nesting, arXiv:1106.5036 [math.CO], 2011-2012.

Example

There are 4213597 partitions of 12 elements, but a(12)=4213597 because the partition {1,12}{2,11}{3,10}{4,9}{5,8}{6,7} has a 6-nesting.

Crossrefs

Cf. A108304, A108305, A192126.

Sequence in context: A287260 A287672 A203641 * A287673 A203642 A192867

Adjacent sequences: A192124 A192125 A192126 * A192128 A192129 A192130

Keyword

nonn

Author

Marni Mishna, Jun 23 2011

Status

approved