This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330677 #6 Apr 27 2020 09:43:15
%S A330677 1,1,1,2,11,81,859
%N A330677 Number of non-isomorphic balanced reduced multisystems of weight n and maximum depth whose leaves (which are multisets of atoms) are sets.
%C A330677 A balanced reduced multisystem is either a finite multiset, or a multiset partition with at least two parts, not all of which are singletons, of a balanced reduced multisystem. The weight of an atom is 1, while the weight of a multiset is the sum of weights of its elements.
%e A330677 Non-isomorphic representatives of the a(0) = 1 through a(4) = 11 multisystems:
%e A330677 {} {1} {1,2} {{1},{1,2}} {{{1}},{{1},{1,2}}}
%e A330677 {{1},{2,3}} {{{1}},{{1},{2,3}}}
%e A330677 {{{1,2}},{{1},{1}}}
%e A330677 {{{1}},{{2},{1,2}}}
%e A330677 {{{1,2}},{{1},{2}}}
%e A330677 {{{1}},{{2},{1,3}}}
%e A330677 {{{1,2}},{{1},{3}}}
%e A330677 {{{1}},{{2},{3,4}}}
%e A330677 {{{1,2}},{{3},{4}}}
%e A330677 {{{2}},{{1},{1,3}}}
%e A330677 {{{2,3}},{{1},{1}}}
%Y A330677 The version with all distinct atoms is A000111.
%Y A330677 Non-isomorphic set multipartitions are A049311.
%Y A330677 The (non-maximal) tree version is A330626.
%Y A330677 Allowing leaves to be multisets gives A330663.
%Y A330677 The case with prescribed degrees is A330664.
%Y A330677 The version allowing all depths is A330668.
%Y A330677 Cf. A000669, A001678, A004114, A005121, A007716, A141268, A283877, A306186, A330465, A330470, A330624.
%K A330677 nonn,more
%O A330677 0,4
%A A330677 _Gus Wiseman_, Dec 30 2019