cp's OEIS Frontend

A319557 Number of non-isomorphic strict connected multiset partitions of weight n.

%I A319557 #16 Jan 21 2023 17:58:25
%S A319557 1,1,2,5,12,30,91,256,823,2656,9103,31876,116113,432824,1659692,
%T A319557 6508521,26112327,106927561,446654187,1900858001,8236367607,
%U A319557 36306790636,162724173883,741105774720,3428164417401,16099059101049,76722208278328,370903316203353,1818316254655097
%N A319557 Number of non-isomorphic strict connected multiset partitions of weight n.
%C A319557 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%C A319557 Also the number of non-isomorphic connected T_0 multiset partitions of weight n. In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. The T_0 condition means that there are no equivalent vertices.
%H A319557 Andrew Howroyd, <a href="/A319557/b319557.txt">Table of n, a(n) for n = 0..50</a>
%F A319557 Inverse Euler transform of A316980.
%e A319557 Non-isomorphic representatives of the a(4) = 12 strict connected multiset partitions:
%e A319557     {{1,1,1,1}}
%e A319557     {{1,1,2,2}}
%e A319557     {{1,2,2,2}}
%e A319557     {{1,2,3,3}}
%e A319557     {{1,2,3,4}}
%e A319557    {{1},{1,1,1}}
%e A319557    {{1},{1,2,2}}
%e A319557    {{2},{1,2,2}}
%e A319557    {{3},{1,2,3}}
%e A319557    {{1,2},{2,2}}
%e A319557    {{1,3},{2,3}}
%e A319557   {{1},{2},{1,2}}
%e A319557 Non-isomorphic representatives of the a(4) = 12 connected T_0 multiset partitions:
%e A319557      {{1,1,1,1}}
%e A319557      {{1,2,2,2}}
%e A319557     {{1},{1,1,1}}
%e A319557     {{1},{1,2,2}}
%e A319557     {{2},{1,2,2}}
%e A319557     {{1,1},{1,1}}
%e A319557     {{1,2},{2,2}}
%e A319557     {{1,3},{2,3}}
%e A319557    {{1},{1},{1,1}}
%e A319557    {{1},{2},{1,2}}
%e A319557    {{2},{2},{1,2}}
%e A319557   {{1},{1},{1},{1}}
%Y A319557 Cf. A007716, A007718, A049311, A056156, A283877, A316980.
%Y A319557 Cf. A319558, A319559, A319560, A319564, A319565, A319566, A319567.
%K A319557 nonn
%O A319557 0,3
%A A319557 _Gus Wiseman_, Sep 23 2018
%E A319557 Terms a(11) and beyond from _Andrew Howroyd_, Jan 19 2023