A316981 Number of non-isomorphic strict multiset partitions of weight n with no equivalent vertices.

1, 1, 2, 6, 15, 40, 121

Offset

0,3

Comments

Also the number of nonnegative integer n X n matrices with sum of elements equal to n, under row and column permutations, with no equal rows and no equal columns.

In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second.

Links

Table of n, a(n) for n=0..6.

Example

Non-isomorphic representatives of the a(3) = 6 strict multiset partitions with no equivalent vertices (first column) and their duals (second column):
      (111) <-> (111)
      (122) <-> (1)(11)
    (1)(11) <-> (122)
    (1)(22) <-> (1)(22)
    (2)(12) <-> (2)(12)
  (1)(2)(3) <-> (1)(2)(3)

Crossrefs

Cf. A000009, A001055, A007716, A007717, A020555, A045778.

Cf. A316974, A316978, A316979, A316980, A316983.

Sequence in context: A001654 A062106 A206000 * A319560 A061322 A004664

Adjacent sequences: A316978 A316979 A316980 * A316982 A316983 A316984

Keyword

nonn,more

Author

Gus Wiseman, Jul 18 2018

Status

approved