%I #6 Apr 18 2024 09:32:47
%S 1,2,3,6,11,21,40,77,144,279
%N Number of non-quanimous subsets of {1..n} containing n, meaning there is only one set partition with equal block-sums.
%e The set s = {3,4,6,8,9} has set partitions {{3,4,6,8,9}} and {{3,4,8},{6,9}} with equal block-sums, so s is not counted under a(9).
%e The a(1) = 1 through a(5) = 11 subsets:
%e {1} {2} {3} {4} {5}
%e {1,2} {1,3} {1,4} {1,5}
%e {2,3} {2,4} {2,5}
%e {3,4} {3,5}
%e {1,2,4} {4,5}
%e {2,3,4} {1,2,5}
%e {1,3,5}
%e {2,4,5}
%e {3,4,5}
%e {1,2,3,5}
%e {1,3,4,5}
%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t Table[Length[Select[Subsets[Range[n]], MemberQ[#,n]&&Length[Select[sps[#],SameQ@@Total/@#&]]==1&]],{n,10}]
%Y First differences of A371789, complement counted by A371796.
%Y The "bi-" version is A371793, complement A232466.
%Y The complement is counted by A371797.
%Y A371736 counts non-quanimous strict partitions.
%Y A371737 counts quanimous strict partitions.
%Y A371783 counts k-quanimous partitions.
%Y A371791 counts biquanimous subsets, complement A371792.
%Y Cf. A002219, A035470, A038041, A275972, A316402, A321451, A321452.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Apr 17 2024