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A108800 Number of nonisomorphic systems enumerated by A102895.

%I A108800 #27 Aug 10 2019 17:38:12
%S A108800 1,2,6,28,330,28960,216562364,5592326182940100
%N A108800 Number of nonisomorphic systems enumerated by A102895.
%C A108800 Also the number of non-isomorphic sets of sets with {} that are closed under intersection. Also the number of non-isomorphic set-systems (without {}) covering n + 1 vertices and closed under intersection. - _Gus Wiseman_, Aug 05 2019
%H A108800 M. Habib and L. Nourine, <a href="https://doi.org/10.1016/j.disc.2004.11.010">The number of Moore families on n = 6</a>, Discrete Math., 294 (2005), 291-296.
%F A108800 a(n > 0) = 2 * A108798(n).
%e A108800 From _Gus Wiseman_, Aug 02 2019: (Start)
%e A108800 Non-isomorphic representatives of the a(0) = 1 through a(3) = 28 sets of sets with {} that are closed under intersection:
%e A108800   {}  {}     {}            {}
%e A108800       {}{1}  {}{1}         {}{1}
%e A108800              {}{12}        {}{12}
%e A108800              {}{1}{2}      {}{123}
%e A108800              {}{2}{12}     {}{1}{2}
%e A108800              {}{1}{2}{12}  {}{1}{23}
%e A108800                            {}{2}{12}
%e A108800                            {}{3}{123}
%e A108800                            {}{1}{2}{3}
%e A108800                            {}{23}{123}
%e A108800                            {}{1}{2}{12}
%e A108800                            {}{1}{3}{23}
%e A108800                            {}{2}{3}{123}
%e A108800                            {}{3}{13}{23}
%e A108800                            {}{1}{23}{123}
%e A108800                            {}{3}{23}{123}
%e A108800                            {}{1}{2}{3}{23}
%e A108800                            {}{1}{2}{3}{123}
%e A108800                            {}{2}{3}{13}{23}
%e A108800                            {}{1}{3}{23}{123}
%e A108800                            {}{2}{3}{23}{123}
%e A108800                            {}{3}{13}{23}{123}
%e A108800                            {}{1}{2}{3}{13}{23}
%e A108800                            {}{1}{2}{3}{23}{123}
%e A108800                            {}{2}{3}{13}{23}{123}
%e A108800                            {}{1}{2}{3}{12}{13}{23}
%e A108800                            {}{1}{2}{3}{13}{23}{123}
%e A108800                            {}{1}{2}{3}{12}{13}{23}{123}
%e A108800 (End)
%Y A108800 Except a(0) = 1, first differences of A193675.
%Y A108800 The connected case (i.e., with maximum) is A108798.
%Y A108800 The same for union instead of intersection is (also) A108798.
%Y A108800 The labeled version is A102895.
%Y A108800 The case also closed under union is A326898.
%Y A108800 The covering case is A326883.
%Y A108800 Cf. A001930, A102894, A102896, A102897, A193674, A326880, A326881.
%K A108800 nonn,more
%O A108800 0,2
%A A108800 _Don Knuth_, Jul 01 2005
%E A108800 a(6) added (using A193675) by _N. J. A. Sloane_, Aug 02 2011
%E A108800 Changed a(0) from 2 to 1 by _Gus Wiseman_, Aug 02 2019
%E A108800 a(7) added (using A108798) by _Andrew Howroyd_, Aug 10 2019