A319793 Number of non-isomorphic connected strict multiset partitions (sets of multisets) of weight n with empty intersection.

1, 0, 0, 0, 1, 4, 24, 96, 412, 1607, 6348, 24580, 96334, 378569, 1508220, 6079720, 24879878, 103335386, 436032901, 1869019800, 8139613977, 36008825317, 161794412893, 738167013847, 3418757243139, 16068569129711, 76622168743677, 370571105669576, 1817199912384794

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) = A319557(n) - A316980(n) + A319077(n). - Andrew Howroyd, May 31 2023

Example

Non-isomorphic representatives of the a(4) = 1 through a(5) = 4 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}}

Crossrefs

Cf. A007716, A007718, A056156, A281116, A283877, A316980, A317752, A317755, A317757, A319616.

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

Sequence in context: A119878 A054603 A100381 * A091143 A119920 A100738

Adjacent sequences: A319790 A319791 A319792 * A319794 A319795 A319796

Keyword

nonn

Author

Gus Wiseman, Sep 27 2018

Extensions

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

Status

approved