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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 29 2018
EXTENSIONS
a(11) onwards from Andrew Howroyd, Jan 27 2024
STATUS
approved