This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A192128 #30 Jul 22 2025 12:11:48
%S A192128 1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,
%T A192128 190899321,1382958475,10480139391,82864788832,682074818390,
%U A192128 5832698911490
%N A192128 Number of set partitions of {1, ..., n} that avoid 7-nestings.
%C A192128 This is equal to the number of set partitions of {1, ..., n} that avoid 7-crossings.
%C A192128 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]
%H A192128 M. Bousquet-Mélou and G. Xin, <a href="https://arxiv.org/abs/math/0506551">On partitions avoiding 3-crossings</a>, arXiv:math/0506551 [math.CO], 2005-2006.
%H A192128 Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, <a href="http://arxiv.org/abs/1108.5615">A generating tree approach to k-nonnesting partitions and permutations</a>, arXiv preprint arXiv:1108.5615 [math.CO], 2011.
%H A192128 W. Chen, E. Deng, R. Du, R. Stanley, and C. Yan, <a href="https://arxiv.org/abs/math/0501230">Crossings and nestings of matchings and partitions</a>, arXiv:math/0501230 [math.CO], 2005.
%H A192128 M. Mishna and L. Yen, <a href="http://arxiv.org/abs/1106.5036">Set partitions with no k-nesting</a>, arXiv:1106.5036 [math.CO], 2011-2012.
%e A192128 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.
%Y A192128 Cf. A000110.
%K A192128 nonn,more
%O A192128 0,3
%A A192128 _Marni Mishna_, Jun 23 2011