A319790 Number of non-isomorphic connected multiset partitions of weight n with empty intersection.

1, 0, 0, 0, 1, 5, 32, 134, 588, 2335, 9335, 36506, 144263, 571238, 2291894, 9300462, 38303796, 160062325, 679333926, 2927951665, 12817221628, 56974693933, 257132512297, 1177882648846, 5475237760563, 25818721638720, 123473772356785, 598687942799298, 2942344764127039

Offset

0,6

Comments

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Formula

a(n) = A007718(n) - A007716(n) + A317757(n). - Andrew Howroyd, May 31 2023

Example

Non-isomorphic representatives of the a(4) = 1 through a(5) = 5 connected multiset partitions:
4:  {{1},{2},{1,2}}
5: {{1},{2},{1,2,2}}
   {{1},{1,2},{2,2}}
   {{2},{3},{1,2,3}}
   {{2},{1,3},{2,3}}
  {{1},{2},{2},{1,2}}

Crossrefs

Cf. A007716, A007718, A049311, A056156, A283877, A317752, A317755, A317757.

Cf. A319077, A319748, A319755, A319778, A319781, A319791.

Sequence in context: A363411 A089574 A077207 * A273623 A359522 A001589

Adjacent sequences: A319787 A319788 A319789 * A319791 A319792 A319793

Keyword

nonn

Author

Gus Wiseman, Sep 27 2018

Extensions

Terms a(11) and beyond from Andrew Howroyd, May 31 2023

Status

approved