A279790 Number of twice-partitions of type (Q,P,Q) and weight n.

1, 1, 3, 3, 5, 11, 12, 18, 24, 49, 53, 82, 102, 149, 236, 297, 392, 540, 702, 924, 1423, 1723, 2318, 3016, 3969, 5037, 6647, 9285, 11448, 15048, 19143, 24695, 31288, 40075, 50014, 68583, 83056, 107252, 133796, 171565

Offset: 1

Author

Gus Wiseman, Dec 18 2016

Keywords

• nonn

Comments

Also number of ways to choose a sum-preserving permutation of a set partition of a strict partition of n.

Examples

			The a(6)=11 twice-partitions are:
((6)),
((5)(1)), ((51)),
((4)(2)), ((42)),
((3)(2)(1)), ((3)(21)), ((21)(3)), ((31)(2)), ((32)(1)), ((321)).
		

Links

• Gus Wiseman, Sequences enumerating triangles of integer partitions

Crossrefs

Cf. A063834, A279791.

Programs

Mathematica

nn=20;
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Total[Sum[Times@@Factorial/@Length/@Split[Sort[Total/@ptn]],{ptn,sps[Sort[#]]}]&/@Select[IntegerPartitions[n],UnsameQ@@#&]],{n,nn}]