%I #20 Nov 20 2023 09:16:08

%S 1,3,17,179,3835,200082,29610804,13702979132,20677458750966,

%T 103609939177198046,1745061194503344181714,99860890306900024150675406,

%U 19611238933283757244479826044874,13340750149227624084760722122669739026,31706433098827528779057124372265863803044450

%N Number of binary n X n matrices with no zero rows or columns, up to row and column permutation.

%C Also the number of non-isomorphic set multipartitions (multisets of sets) with n parts and n vertices. - _Gus Wiseman_, Nov 18 2018

%H Andrew Howroyd, <a href="/A054976/b054976.txt">Table of n, a(n) for n = 1..50</a>

%F a(n) = A002724(n) - 2*A002725(n-1) + A002724(n-1).

%e From _Gus Wiseman_, Nov 18 2018: (Start)

%e Inequivalent representatives of the a(3) = 17 matrices:

%e 100 100 100 100 100 010 010 001 001 001 001 110 101 101 011 011 111

%e 100 010 001 011 011 001 101 001 101 011 111 101 011 011 011 111 111

%e 011 001 011 011 111 111 011 111 011 111 111 011 011 111 111 111 111

%e Non-isomorphic representatives of the a(1) = 1 through a(3) = 17 set multipartitions:

%e {{1}} {{1},{2}} {{1},{2},{3}}

%e {{2},{1,2}} {{1},{1},{2,3}}

%e {{1,2},{1,2}} {{1},{3},{2,3}}

%e {{1},{2,3},{2,3}}

%e {{2},{1,3},{2,3}}

%e {{2},{3},{1,2,3}}

%e {{3},{1,3},{2,3}}

%e {{3},{3},{1,2,3}}

%e {{1,2},{1,3},{2,3}}

%e {{1},{2,3},{1,2,3}}

%e {{1,3},{2,3},{2,3}}

%e {{3},{2,3},{1,2,3}}

%e {{1,3},{2,3},{1,2,3}}

%e {{2,3},{2,3},{1,2,3}}

%e {{3},{1,2,3},{1,2,3}}

%e {{2,3},{1,2,3},{1,2,3}}

%e {{1,2,3},{1,2,3},{1,2,3}}

%e (End)

%t A002724 = Cases[Import["https://oeis.org/A002724/b002724.txt", "Table"], {_, _}][[All, 2]];

%t A002725 = Cases[Import["https://oeis.org/A002725/b002725.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := A002724[[n + 1]] - 2 A002725[[n]] + A002724[[n]];

%t a /@ Range[1, 13] (* _Jean-François Alcover_, Sep 14 2019 *)

%Y Column sums of A057150.

%Y Cf. A007716, A048291 (labeled), A049311, A057149, A057151, A104601, A104602, A319616, A320808.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, May 27 2000

%E More terms from _David Wasserman_, Mar 06 2002

%E Terms a(14) and beyond from _Andrew Howroyd_, Apr 11 2020