A192867 Number of set partitions of {1, ..., n} that avoid enhanced 7-crossings (or enhanced 7-nestings)

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644436, 190899266, 1382956734, 10480097431, 82863928963, 682058946982, 5832425824171, 51718812364549

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 27644437 partitions of 13 elements, but a(13)=27644436 because the partition {1,13}{2,12}{3,11}{4,10}{5,9}{6,8} {7} has an enhanced 7-nesting.

Crossrefs

Cf. A000110, A108307, A192855, A192865, A192866.

Sequence in context: A192127 A287673 A203642 * A203643 A192128 A203644

Adjacent sequences: A192864 A192865 A192866 * A192868 A192869 A192870

Keyword

nonn

Author

Marni Mishna, Jul 11 2011

Status

approved