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 A294788 #9 Nov 16 2017 05:31:03
%S A294788 1,1,1,1,1,3,1,3,1,3,1,5,1,3,3,3,1,5,1,5,3,3,1,12,1,3,3,5,1,12,1,5,3,
%T A294788 3,3,13,1,3,3,12,1,12,1,5,5,3,1,19,1,5,3,5,1,12,3,12,3,3,1,26,1,3,5,
%U A294788 11,3,12,1,5,3,12,1,26,1,3,5,5,3,12,1,19,3,3
%N A294788 Number of twice-factorizations of type (Q,P,Q) and product n.
%C A294788 a(n) is the number of ways to choose a product-preserving permutation of a set partition of a factorization of n into distinct factors greater than one.
%e A294788 The a(36) = 13 twice-factorizations are: (2)*(3)*(6), (2)*(3*6), (6)*(2*3), (2*3)*(6), (2*6)*(3), (2*3*6), (2)*(18), (2*18), (3)*(12), (3*12), (4)*(9), (4*9), (36).
%t A294788 nn=100;
%t A294788 sfs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[sfs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A294788 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A294788 Table[Total[Sum[Times@@Factorial/@Length/@Split[Sort[Times@@@f]],{f,sps[Sort[#]]}]&/@sfs[n]],{n,nn}]
%Y A294788 Cf. A001055, A063834, A279790, A281113, A294786, A294787.
%K A294788 nonn
%O A294788 1,6
%A A294788 _Gus Wiseman_, Nov 08 2017