A192128 Number of set partitions of {1, ..., n} that avoid 7-nestings.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899321, 1382958475, 10480139391, 82864788832, 682074818390, 5832698911490

Offset: 0

Author

Marni Mishna, Jun 23 2011

Keywords

• nonn
• more

Comments

This is equal to the number of set partitions of {1, ..., n} that avoid 7-crossings.

The first 14 terms coincide with terms of A000110. Without avoidance of 7-crossings, the two sequences would be identical. [Alexander R. Povolotsky, Sep 19 2011]

Examples

			There are 190899322 partitions of 14 elements, but a(14)=190899321 because the partition {1,14}{2,13}{3,12}{4,11}{5,10}{6,9}{7,8} has a 7-nesting.
		

Links

• 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.

Crossrefs

Cf. A000110.