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%I #8 Jun 22 2019 14:37:33
%S 1,1,1,3,3,5,10,14,25,44,71,128,231,411,740,1352,2481,4570,8390,15550,
%T 29103,54345,101312,190316,359827,679051,1279956,2426200,4621174,
%U 8789565,16701225,31871629,61052515,116818123,223333533,428435056,824395640,1584833707,3044562148,5865073390,11326741619,21857561924
%N Number of minimal subsets of {1..n} containing n whose sum is greater than or equal to the sum of their complement.
%e The a(1) = 1 through a(8) = 14 subsets:
%e {1} {2} {3} {1,4} {3,5} {5,6} {1,6,7} {3,7,8}
%e {2,4} {4,5} {1,4,6} {2,5,7} {4,6,8}
%e {3,4} {1,2,5} {2,3,6} {2,6,7} {4,7,8}
%e {2,4,6} {3,4,7} {5,6,8}
%e {3,4,6} {3,5,7} {5,7,8}
%e {3,6,7} {6,7,8}
%e {4,5,7} {1,2,7,8}
%e {4,6,7} {1,3,6,8}
%e {5,6,7} {1,4,5,8}
%e {1,2,4,7} {2,3,5,8}
%e {2,3,6,8}
%e {2,4,5,8}
%e {3,4,5,8}
%e {1,2,3,4,8}
%t fasmin[y_]:=Complement[y,Union@@Table[Union[s,#]&/@Rest[Subsets[Complement[Union@@y,s]]],{s,y}]];
%t Table[Length[fasmin[Select[Subsets[Range[n]],MemberQ[#,n]&&Plus@@#>=Plus@@Complement[Range[n],#]&]]],{n,10}]
%Y Cf. A053632, A057567, A057568, A059529, A063865, A326152, A326173, A326174.
%K nonn
%O 1,4
%A _Gus Wiseman_, Jun 11 2019
%E a(15)-a(42) from _Bert Dobbelaere_, Jun 22 2019
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