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A327438 Irregular triangle read by rows with trailing zeros removed where T(n,k) is the number of unlabeled antichains of nonempty subsets of {1..n} with spanning edge-connectivity k.

%I A327438 #8 Sep 11 2019 20:22:58
%S A327438 1,1,1,3,1,6,2,1,15,7,5,2,52,53,62,31,9,1,1
%N A327438 Irregular triangle read by rows with trailing zeros removed where T(n,k) is the number of unlabeled antichains of nonempty subsets of {1..n} with spanning edge-connectivity k.
%C A327438 An antichain is a set of sets, none of which is a subset of any other.
%C A327438 The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.
%e A327438 Triangle begins:
%e A327438    1
%e A327438    1  1
%e A327438    3  1
%e A327438    6  2  1
%e A327438   15  7  5  2
%e A327438   52 53 62 31  9  1  1
%e A327438 The antichains counted in row n = 4 are the following:
%e A327438   0             {1234}         {12}{134}{234}     {123}{124}{134}{234}
%e A327438   {1}           {12}{134}      {123}{124}{134}    {12}{13}{14}{23}{24}{34}
%e A327438   {12}          {123}{124}     {12}{13}{24}{34}
%e A327438   {123}         {12}{13}{14}   {12}{13}{14}{234}
%e A327438   {1}{2}        {12}{13}{24}   {12}{13}{14}{23}{24}
%e A327438   {1}{23}       {12}{13}{234}
%e A327438   {12}{13}      {12}{13}{14}{23}
%e A327438   {1}{234}
%e A327438   {12}{34}
%e A327438   {1}{2}{3}
%e A327438   {1}{2}{34}
%e A327438   {2}{13}{14}
%e A327438   {12}{13}{23}
%e A327438   {1}{2}{3}{4}
%e A327438   {4}{12}{13}{23}
%Y A327438 Row sums are A306505.
%Y A327438 Column k = 0 is A327437.
%Y A327438 The labeled version is A327352.
%Y A327438 Cf. A014466, A052446, A327062, A327071, A327103, A327111, A327144, A327352, A327353.
%K A327438 nonn,tabf,more
%O A327438 0,4
%A A327438 _Gus Wiseman_, Sep 11 2019