A192865 -id:A192865 - cp's OEIS frontend

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

Marni Mishna, Jul 11 2011

nonn

			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.

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

Cf. A000110, A108307, A192855, A192865.

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

Original entry on oeis.org

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

Offset: 0

Marni Mishna, Jul 11 2011

nonn

			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.

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

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

cp's OEIS Frontend

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

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