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 A318128 #5 Aug 19 2018 18:19:33
%S A318128 1,0,2,84,31478,2147000136,9223371998203475474,
%T A318128 170141183460469231537996491257596836636,
%U A318128 57896044618658097711785492504343953922551603929769020459976077632195066756398
%N A318128 Number of set-systems (finite sets of finite nonempty sets) with union {1,2,...,n} and intersection {}.
%F A318128 Inverse binomial transform of A318129.
%e A318128 The a(2) = 2 set-systems are {{1},{2}}, and {{1},{2},{1,2}}.
%t A318128 Table[Length[Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#===Range[n],Intersection@@#=={}]&]],{n,4}]
%Y A318128 Cf. A000371, A001146, A003465, A119563, A131288.
%Y A318128 Cf. A318128, A318129, A318130, A318131, A318132.
%K A318128 nonn
%O A318128 0,3
%A A318128 _Gus Wiseman_, Aug 18 2018