

A192128


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


0



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

0,3


COMMENTS

This is equal to the number of set partitions of {1, ..., n} that avoid 7crossings.
The first 14 terms coincide with terms of A000110. Without avoidance of 7crossings, the two sequences would be identical. [Alexander R. Povolotsky, Sep 19 2011]


LINKS

Table of n, a(n) for n=0..19.
M. BousquetMÃ©lou and G. Xin, On partitions avoiding 3crossings, arXiv:math/0506551 [math.CO], 20052006.
Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, A generating tree approach to knonnesting 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 knesting, arXiv:1106.5036 [math.CO], 20112012.


EXAMPLE

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 7nesting.


CROSSREFS

Cf. A000110.
Sequence in context: A203642 A192867 A203643 * A203644 A203645 A203646
Adjacent sequences: A192125 A192126 A192127 * A192129 A192130 A192131


KEYWORD

nonn,more


AUTHOR

Marni Mishna, Jun 23 2011


STATUS

approved



