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 A321467 #12 Nov 13 2018 12:54:58
%S A321467 1,1,1,2,5,15,47,183,719,3329,14990,83798,393864,2518898
%N A321467 Number of factorizations of n! into factors > 1 that can be obtained by taking the block-products of some set partition of {2,3,...,n}.
%C A321467 a(n) is the number of factorizations coarser than (2*3*...*n) in the poset of factorizations of n! into factors > 1, ordered by refinement.
%e A321467 The a(1) = 1 through a(5) = 15 factorizations:
%e A321467 () (2) (6) (24) (120)
%e A321467 (2*3) (3*8) (2*60)
%e A321467 (4*6) (3*40)
%e A321467 (2*12) (4*30)
%e A321467 (2*3*4) (5*24)
%e A321467 (6*20)
%e A321467 (8*15)
%e A321467 (10*12)
%e A321467 (3*5*8)
%e A321467 (4*5*6)
%e A321467 (2*3*20)
%e A321467 (2*4*15)
%e A321467 (2*5*12)
%e A321467 (3*4*10)
%e A321467 (2*3*4*5)
%e A321467 For example, 10*12 = (2*5)*(3*4), so (10*12) is counted under a(5).
%t A321467 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A321467 Table[Length[Union[Sort/@Apply[Times,sps[Range[2,n]],{2}]]],{n,10}]
%Y A321467 Dominated by A000110.
%Y A321467 Cf. A001055, A066723, A157612, A242422, A265947, A317141, A317144, A317145, A317534, A321468, A321470, A321471, A321472, A321514.
%K A321467 nonn,more
%O A321467 0,4
%A A321467 _Gus Wiseman_, Nov 11 2018