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 A369926 #11 Feb 06 2024 19:32:01 %S A369926 1,0,0,0,1,0,3,1,9,8,34,45,177,324,1048,2566,8050,22840,73562,231978, %T A369926 780221,2653042,9377141,33820014,125473936,475719042,1846424607, %U A369926 7317819857,29611827086,122190972442,513900819816,2201109101784,9595815668795,42553843201446,191861748624324,879049648551947 %N A369926 Number of non-isomorphic set multipartitions (multisets of sets) of weight n without endpoints or singletons. %C A369926 A singleton is a part of size 1. An endpoint is a vertex that appears in only one part. %C A369926 a(n) is also the number of binary matrices with a total of n 1's and every row and column sum at least 2 up to permutation of rows and columns. %H A369926 Andrew Howroyd, <a href="/A369926/b369926.txt">Table of n, a(n) for n = 0..50</a> %e A369926 The a(8) = 9 matrices are: %e A369926 [1 1 1 1] [1 1 1] [1 1 1 0] [1 1 1 1] %e A369926 [1 1 1 1] [1 1 1] [1 1 0 1] [1 1 0 0] %e A369926 [1 1 0] [0 0 1 1] [0 0 1 1] %e A369926 . %e A369926 [1 1] [1 1 0] [1 1 0] [1 1 0 0] [1 1 0 0] %e A369926 [1 1] [1 1 0] [1 1 0] [1 1 0 0] [1 0 1 0] %e A369926 [1 1] [1 0 1] [1 0 1] [0 0 1 1] [0 1 0 1] %e A369926 [1 1] [1 0 1] [0 1 1] [0 0 1 1] [0 0 1 1] %o A369926 (PARI) Vec(G(25,1)) \\ G defined in A369927. %Y A369926 Row sums of A369927. %Y A369926 A321677 is the case without singletons but allowing endpoints (or by duality without endpoints but allowing singletons). %Y A369926 Cf. A330055 (set-systems). %K A369926 nonn %O A369926 0,7 %A A369926 _Andrew Howroyd_, Feb 06 2024