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 A306551 #6 Feb 24 2019 01:54:44
%S A306551 1,1,2,5,15,52,202,863,3999,19880,105134,587479,3449505
%N A306551 Number of non-double-crossing set partitions of {1,...,n}.
%C A306551 Two blocks of a set partitions double-cross each other if they are of the form {{...a...b...c...},{...x...y...z...}} for some a < x < b < y < c < z or x < a < y < b < z < c.
%H A306551 Kenneth J. Dykema, <a href="http://arxiv.org/abs/1602.03469">Generating functions for purely crossing partitions</a>, arXiv:1602.03469 [math.CO], 2016.
%e A306551 Most small set partitions are not double-crossing. The smallest that is double-crossing is {{1,3,5},{2,4,6}}.
%t A306551 nonXXQ[stn_]:=!MatchQ[stn,{___,{___,a_,___,b_,___,c_,___},___,{___,x_,___,y_,___,z_,___},___}/;a<x<b<y<c<z||x<a<y<b<z<c];
%t A306551 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A306551 Table[Length[Select[sps[Range[n]],nonXXQ]],{n,0,8}]
%Y A306551 Cf. A000108, A000110, A001263, A002061, A005493, A007297, A016098, A054726, A099947, A324166, A324167, A324172, A324324.
%K A306551 nonn,more
%O A306551 0,3
%A A306551 _Gus Wiseman_, Feb 23 2019