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 A320812 #10 Jan 16 2023 14:36:50
%S A320812 1,0,2,3,10,23,79,204,670,1974,6521,21003,71944,248055,888565,3240552,
%T A320812 12152093,46527471,182337383,729405164,2979114723,12407307929,
%U A320812 52670334237,227725915268,1002285201807,4487915293675,20434064047098,94559526594316,444527729321513
%N A320812 Number of non-isomorphic aperiodic multiset partitions of weight n with no singletons.
%C A320812 A multiset is aperiodic if its multiplicities are relatively prime.
%C A320812 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 A320812 Andrew Howroyd, <a href="/A320812/b320812.txt">Table of n, a(n) for n = 0..50</a>
%F A320812 a(n) = Sum_{d|n} mu(d)*A302545(n/d) for n > 0. - _Andrew Howroyd_, Jan 16 2023
%e A320812 Non-isomorphic representatives of the a(2) = 2 through a(5) = 23 multiset partitions:
%e A320812 {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}}
%e A320812 {{1,2}} {{1,2,2}} {{1,1,2,2}} {{1,1,2,2,2}}
%e A320812 {{1,2,3}} {{1,2,2,2}} {{1,2,2,2,2}}
%e A320812 {{1,2,3,3}} {{1,2,2,3,3}}
%e A320812 {{1,2,3,4}} {{1,2,3,3,3}}
%e A320812 {{1,1},{2,2}} {{1,2,3,4,4}}
%e A320812 {{1,2},{2,2}} {{1,2,3,4,5}}
%e A320812 {{1,2},{3,3}} {{1,1},{1,1,1}}
%e A320812 {{1,2},{3,4}} {{1,1},{1,2,2}}
%e A320812 {{1,3},{2,3}} {{1,1},{2,2,2}}
%e A320812 {{1,1},{2,3,3}}
%e A320812 {{1,1},{2,3,4}}
%e A320812 {{1,2},{1,2,2}}
%e A320812 {{1,2},{2,2,2}}
%e A320812 {{1,2},{2,3,3}}
%e A320812 {{1,2},{3,3,3}}
%e A320812 {{1,2},{3,4,4}}
%e A320812 {{1,2},{3,4,5}}
%e A320812 {{1,3},{2,3,3}}
%e A320812 {{1,4},{2,3,4}}
%e A320812 {{2,2},{1,2,2}}
%e A320812 {{2,3},{1,2,3}}
%e A320812 {{3,3},{1,2,3}}
%Y A320812 Cf. A000740, A000837, A007716, A007916, A100953, A301700, A302545, A303386, A303546, A303707, A303708, A320797-A320813, A321390.
%K A320812 nonn
%O A320812 0,3
%A A320812 _Gus Wiseman_, Nov 08 2018
%E A320812 Terms a(11) and beyond from _Andrew Howroyd_, Jan 16 2023