cp's OEIS Frontend

A319791 Number of non-isomorphic connected set multipartitions (multisets of sets) of weight n with empty intersection.

%I A319791 #9 May 31 2023 10:49:13
%S A319791 1,0,0,0,1,3,14,38,125,360,1107,3297,10292,32134,103759,340566,
%T A319791 1148150,3951339,13925330,50122316,184365292,692145409,2651444318,
%U A319791 10356184440,41224744182,167150406897,689998967755,2898493498253,12384852601731,53804601888559,237566072006014
%N A319791 Number of non-isomorphic connected set multipartitions (multisets of sets) of weight n with empty intersection.
%C A319791 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%H A319791 Andrew Howroyd, <a href="/A319791/b319791.txt">Table of n, a(n) for n = 0..50</a>
%F A319791 a(n) = A056156(n) - A049311(n) + A319748(n). - _Andrew Howroyd_, May 31 2023
%e A319791 Non-isomorphic representatives of the a(4) = 1 through a(6) = 14 set multipartitions:
%e A319791 4:    {{1},{2},{1,2}}
%e A319791 5:   {{2},{3},{1,2,3}}
%e A319791      {{2},{1,3},{2,3}}
%e A319791     {{1},{2},{2},{1,2}}
%e A319791 6:  {{1},{1,4},{2,3,4}}
%e A319791     {{1},{2,3},{1,2,3}}
%e A319791     {{3},{4},{1,2,3,4}}
%e A319791     {{3},{1,4},{2,3,4}}
%e A319791     {{1,2},{1,3},{2,3}}
%e A319791     {{1,3},{2,4},{3,4}}
%e A319791    {{1},{2},{3},{1,2,3}}
%e A319791    {{1},{2},{1,2},{1,2}}
%e A319791    {{1},{2},{1,3},{2,3}}
%e A319791    {{2},{2},{1,3},{2,3}}
%e A319791    {{2},{3},{3},{1,2,3}}
%e A319791    {{2},{3},{1,3},{2,3}}
%e A319791   {{1},{1},{2},{2},{1,2}}
%e A319791   {{1},{2},{2},{2},{1,2}}
%Y A319791 Cf. A007716, A007718, A049311, A056156, A281116, A283877, A317752, A317755, A317757.
%Y A319791 Cf. A319077, A319748, A319755, A319778, A319781, A319790.
%K A319791 nonn
%O A319791 0,6
%A A319791 _Gus Wiseman_, Sep 27 2018
%E A319791 Terms a(11) and beyond from _Andrew Howroyd_, May 31 2023