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

0,3

Links

Table of n, a(n) for n=0..35.

Formula

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

Example

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)

Mathematica

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

Prog

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

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.

Sequence in context: A087134 A370494 A036689 * A226326 A139115 A193538

Adjacent sequences: A355387 A355388 A355389 * A355391 A355392 A355393

Keyword

nonn

Author

Gus Wiseman, Jul 04 2022

Status

approved