A355390 Number of ordered pairs of distinct integer partitions of n.

0, 0, 2, 6, 20, 42, 110, 210, 462, 870, 1722, 3080, 5852, 10100, 18090, 30800, 53130, 87912, 147840, 239610, 392502, 626472, 1003002, 1573770, 2479050, 3831806, 5931660, 9057090, 13819806, 20834660, 31399212, 46806122, 69697452, 102870306, 151523790, 221488806

Offset: 0

Author

Gus Wiseman, Jul 04 2022

Keywords

• nonn

Examples

			The a(0) = 0 through a(3) = 6 pairs:
  .  .  (11)(2)  (21)(3)
        (2)(11)  (3)(21)
                 (111)(3)
                 (3)(111)
                 (111)(21)
                 (21)(111)
		

Crossrefs

Without distinctness we have A001255, unordered A086737.

The version for compositions is A020522, unordered A006516.

The unordered version is A355389.

A000041 counts partitions, strict A000009.

A001970 counts multiset partitions of partitions.

A063834 counts partitions of each part of a partition.

Cf. A022811, A070933, A316245, A317715, A319910, A323433, A323583, A339006, A355385.

Programs

Mathematica

Table[Length[Select[Tuples[IntegerPartitions[n],2],UnsameQ@@#&]],{n,0,15}]

PARI

a(n) = 2*binomial(numbpart(n), 2); \\ Michel Marcus, Jul 05 2022

Formula

a(n) = 2*A355389(n) = 2*binomial(A000041(n), 2).