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A316980 Number of non-isomorphic strict multiset partitions of weight n. 94
1, 1, 3, 8, 23, 63, 197, 588, 1892, 6140, 20734 (list; graph; refs; listen; history; text; internal format)
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 (or alternatively, with no equal columns).

Also the number of non-isomorphic multiset partitions of weight n with no equivalent vertices. 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..10.

FORMULA

Euler transform of A319557. - Gus Wiseman, Sep 23 2018

EXAMPLE

Non-isomorphic representatives of the a(3) = 8 multiset partitions with no equivalent vertices (first column) and with no equal blocks (second column):

      (111) <-> (111)

      (122) <-> (1)(11)

    (1)(11) <-> (122)

    (1)(22) <-> (1)(22)

    (2)(12) <-> (2)(12)

  (1)(1)(1) <-> (123)

  (1)(2)(2) <-> (1)(23)

  (1)(2)(3) <-> (1)(2)(3)

CROSSREFS

Cf. A000009, A001055, A007716, A007717, A020555, A045778, A130091.

Cf. A316974, A316978, A316979, A316981, A316983.

Cf. A049311, A059201, A319558, A319560, A319567.

Sequence in context: A248870 A103819 A147484 * A017929 A017930 A305561

Adjacent sequences:  A316977 A316978 A316979 * A316981 A316982 A316983

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 18 2018

EXTENSIONS

a(7) - a(10) from Gus Wiseman, Sep 23 2018

STATUS

approved

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Last modified November 11 15:40 EST 2019. Contains 329016 sequences. (Running on oeis4.)