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 A327019 Number of non-isomorphic set-systems of weight n whose dual is a (strict) antichain. 1
 1, 1, 1, 1, 2, 2, 5, 7, 15, 26, 61 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Also the number of non-isomorphic set-systems where every vertex is the unique common element of some subset of the edges, also called non-isomorphic T_1 set-systems. A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of sets, none of which is a subset of any other. LINKS EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(8) = 15 multiset partitions:   {1}  {1}{2}  {1}{2}{3}  {1}{2}{12}    {1}{2}{3}{23}    {12}{13}{23}                           {1}{2}{3}{4}  {1}{2}{3}{4}{5}  {1}{2}{13}{23}                                                          {1}{2}{3}{123}                                                          {1}{2}{3}{4}{34}                                                          {1}{2}{3}{4}{5}{6} .   {1}{23}{24}{34}        {12}{13}{24}{34}   {3}{12}{13}{23}        {2}{13}{14}{234}   {1}{2}{3}{13}{23}      {1}{2}{13}{24}{34}   {1}{2}{3}{24}{34}      {1}{2}{3}{14}{234}   {1}{2}{3}{4}{234}      {1}{2}{3}{23}{123}   {1}{2}{3}{4}{5}{45}    {1}{2}{3}{4}{1234}   {1}{2}{3}{4}{5}{6}{7}  {1}{2}{34}{35}{45}                          {1}{4}{23}{24}{34}                          {2}{3}{12}{13}{23}                          {1}{2}{3}{4}{12}{34}                          {1}{2}{3}{4}{24}{34}                          {1}{2}{3}{4}{35}{45}                          {1}{2}{3}{4}{5}{345}                          {1}{2}{3}{4}{5}{6}{56}                          {1}{2}{3}{4}{5}{6}{7}{8} CROSSREFS Cf. A007716, A059523, A283877, A293993, A326961, A326965, A326974, A326976, A326977, A326979, A327012, A327018. Sequence in context: A195964 A047083 A238422 * A035085 A208238 A127413 Adjacent sequences:  A327016 A327017 A327018 * A327020 A327021 A327022 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 15 2019 STATUS approved

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Last modified January 26 08:18 EST 2020. Contains 331278 sequences. (Running on oeis4.)