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 A279790 #6 Dec 21 2016 11:05:07
%S A279790 1,1,3,3,5,11,12,18,24,49,53,82,102,149,236,297,392,540,702,924,1423,
%T A279790 1723,2318,3016,3969,5037,6647,9285,11448,15048,19143,24695,31288,
%U A279790 40075,50014,68583,83056,107252,133796,171565
%N A279790 Number of twice-partitions of type (Q,P,Q) and weight n.
%C A279790 Also number of ways to choose a sum-preserving permutation of a set partition of a strict partition of n.
%H A279790 Gus Wiseman, <a href="/A063834/a063834.txt">Sequences enumerating triangles of integer partitions</a>
%e A279790 The a(6)=11 twice-partitions are:
%e A279790 ((6)),
%e A279790 ((5)(1)), ((51)),
%e A279790 ((4)(2)), ((42)),
%e A279790 ((3)(2)(1)), ((3)(21)), ((21)(3)), ((31)(2)), ((32)(1)), ((321)).
%t A279790 nn=20;
%t A279790 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A279790 Table[Total[Sum[Times@@Factorial/@Length/@Split[Sort[Total/@ptn]],{ptn,sps[Sort[#]]}]&/@Select[IntegerPartitions[n],UnsameQ@@#&]],{n,nn}]
%Y A279790 Cf. A063834, A279791.
%K A279790 nonn
%O A279790 1,3
%A A279790 _Gus Wiseman_, Dec 18 2016