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

1,3

Comments

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

Links

Table of n, a(n) for n=1..40.

Gus Wiseman, Sequences enumerating triangles of integer partitions

Example

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)).

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}]

Crossrefs

Cf. A063834, A279791.

Sequence in context: A218354 A286514 A235859 * A338847 A032020 A261962

Adjacent sequences: A279787 A279788 A279789 * A279791 A279792 A279793

Keyword

nonn

Author

Gus Wiseman, Dec 18 2016

Status

approved