A321760 Number of non-isomorphic multiset partitions of weight n with no constant parts or vertices that appear in only one part.

1, 0, 0, 0, 1, 1, 7, 9, 37, 79, 273, 755, 2648, 8432, 29872, 104624, 384759, 1432655, 5502563, 21533141, 86291313, 352654980, 1471073073, 6253397866, 27083003687, 119399628021, 535591458635, 2443030798539, 11326169401988, 53343974825122, 255121588496338

Offset

0,7

Comments

Also the number of nonnegative integer matrices up to row and column permutations with sum of elements equal to n in which every row and column has at least two nonzero entries.

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

Example

Non-isomorphic representatives of the a(4) = 1 through a(7) = 9 multiset partitions:
  {{1,2},{1,2}}  {{1,2},{1,2,2}}  {{1,1,2},{1,2,2}}    {{1,1,2},{1,2,2,2}}
                                  {{1,2},{1,1,2,2}}    {{1,2},{1,1,2,2,2}}
                                  {{1,2},{1,2,2,2}}    {{1,2},{1,2,2,2,2}}
                                  {{1,2,2},{1,2,2}}    {{1,2,2},{1,1,2,2}}
                                  {{1,2,3},{1,2,3}}    {{1,2,2},{1,2,2,2}}
                                  {{1,2},{1,2},{1,2}}  {{1,2,3},{1,2,3,3}}
                                  {{1,2},{1,3},{2,3}}  {{1,2},{1,2},{1,2,2}}
                                                       {{1,2},{1,3},{2,3,3}}
                                                       {{1,3},{2,3},{1,2,3}}

Prog

(PARI) Vec(G(20, 1)) \\ G defined in A369286. - Andrew Howroyd, Jan 28 2024

Crossrefs

Row sums of A369286.

Cf. A001970, A007716, A050535, A055884, A120733, A317533, A320665, A320798, A320801, A320808, A321407.

Sequence in context: A189974 A316184 A359367 * A083203 A082536 A057590

Adjacent sequences: A321757 A321758 A321759 * A321761 A321762 A321763

Keyword

nonn

Author

Gus Wiseman, Nov 29 2018

Extensions

a(11) onwards from Andrew Howroyd, Jan 27 2024

Status

approved