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A321760
Number of non-isomorphic multiset partitions of weight n with no constant parts or vertices that appear in only one part.
10
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 29 2018
EXTENSIONS
a(11) onwards from Andrew Howroyd, Jan 27 2024
STATUS
approved