# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a320806
Showing 1-1 of 1

%I A320806 #5 Nov 07 2018 21:45:34
%S A320806 1,1,1,4,10,39,81,343,903,3223,9989
%N A320806 Number of non-isomorphic multiset partitions of weight n in which each of the parts and each part of the dual, as well as both the multiset union of the parts and the multiset union of the dual parts, is an aperiodic multiset.
%C A320806 Also the number of nonnegative integer matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which (1) the positive entries in each row and column are relatively prime and (2) the row sums and column sums are relatively prime.
%C A320806 The last condition (aperiodicity of the multiset union of the dual) is equivalent to the parts having relatively prime sizes.
%C A320806 A multiset is aperiodic if its multiplicities are relatively prime.
%C A320806 The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
%C A320806 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e A320806 Non-isomorphic representatives of the a(1) = 1 through a(4) = 10 multiset partitions:
%e A320806   {{1}}  {{1},{2}}  {{1},{2,3}}    {{1},{2,3,4}}
%e A320806                     {{2},{1,2}}    {{2},{1,2,2}}
%e A320806                     {{1},{2},{2}}  {{3},{1,2,3}}
%e A320806                     {{1},{2},{3}}  {{1},{1},{2,3}}
%e A320806                                    {{1},{2},{3,4}}
%e A320806                                    {{1},{3},{2,3}}
%e A320806                                    {{2},{2},{1,2}}
%e A320806                                    {{1},{2},{2},{2}}
%e A320806                                    {{1},{2},{3},{3}}
%e A320806                                    {{1},{2},{3},{4}}
%Y A320806 Cf. A000740, A000837, A007716, A007916, A100953, A301700, A303386, A303546, A303707, A303708, A316983, A320800-A320810, A321283.
%K A320806 nonn,more
%O A320806 0,4
%A A320806 _Gus Wiseman_, Nov 07 2018

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE