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 A108305 #32 May 26 2025 18:28:16
%S A108305 1,1,2,5,15,52,203,877,4139,21119,115495,671969,4132936,26723063,
%T A108305 180775027,1274056792,9320514343,70548979894,550945607475,
%U A108305 4427978077331,36544023687590,309088822019071
%N A108305 Number of set partitions of {1, ..., n} that avoid 4-crossings.
%H A108305 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 A108305 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 A108305 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 A108305 Juan B. Gil and Jordan O. Tirrell, <a href="https://arxiv.org/abs/1806.09065">A simple bijection for classical and enhanced k-noncrossing partitions</a>, arXiv:1806.09065 [math.CO], 2018. Also Discrete Mathematics (2019) Article 111705. doi:10.1016/j.disc.2019.111705
%H A108305 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 A108305 There are 4140 partitions of 8 elements, but a(8) = 4139 because the partition (1,5)(2,6)(3,7)(4,8) has a 4-crossing.
%Y A108305 Cf. A108304 (k = 3), (this: k = 4), A192126 (k = 5), A192127 (k = 6), A192128 (k = 7).
%Y A108305 Cf. A192855.
%K A108305 nonn,more
%O A108305 0,3
%A A108305 _Mireille Bousquet-Mélou_, Jun 29 2005
%E A108305 One more value from Burrill et al (2011). - _R. J. Mathar_, May 25 2025