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