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 A321736 Number of non-isomorphic weight-n multiset partitions whose part-sizes are also their vertex-degrees. 5
 1, 1, 2, 4, 9, 17, 42, 92, 231, 579, 1577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of nonnegative integer square matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with the same multiset of row sums as of column sums. 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 Table of n, a(n) for n=0..10. EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 17 multiset partitions: {{1}} {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}} {{1},{2}} {{1},{2,2}} {{1,1},{2,2}} {{1,1},{1,2,2}} {{2},{1,2}} {{1,2},{1,2}} {{1,1},{2,2,2}} {{1},{2},{3}} {{1},{2,2,2}} {{1,2},{1,2,2}} {{2},{1,2,2}} {{1},{2,2,2,2}} {{1},{1},{2,3}} {{2},{1,2,2,2}} {{1},{2},{3,3}} {{1},{2,2},{3,3}} {{1},{3},{2,3}} {{1},{2,3},{2,3}} {{1},{2},{3},{4}} {{1},{2},{3,3,3}} {{1},{3},{2,3,3}} {{2},{1,2},{3,3}} {{2},{1,3},{2,3}} {{3},{3},{1,2,3}} {{1},{2},{2},{3,4}} {{1},{2},{3},{4,4}} {{1},{2},{4},{3,4}} {{1},{2},{3},{4},{5}} CROSSREFS Cf. A000700, A007716, A057150, A120732, A319056, A319616, A320451, A321719, A321721, A321722, A321724, A321732, A321733, A321735, A321739. Sequence in context: A030035 A123431 A049961 * A283315 A024425 A034685 Adjacent sequences: A321733 A321734 A321735 * A321737 A321738 A321739 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 19 2018 STATUS approved

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Last modified December 3 01:55 EST 2023. Contains 367530 sequences. (Running on oeis4.)