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%I #14 Mar 03 2018 22:06:56
%S 1,1,2,6,18,65,258,1156,5558,29029,161942,967921,6110687,40807420,
%T 286177944,2107745450
%N Number of ordered set partitions of {1,...,n} with weakly increasing block-sums.
%e The a(3) = 6 ordered set partitions: (123), (1)(23), (2)(13), (12)(3), (3)(12), (1)(2)(3).
%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t Table[Sum[Times@@Factorial/@Length/@GatherBy[sptn,Total],{sptn,sps[Range[n]]}],{n,8}]
%Y A000110(n) <= a(n) <= A000670(n).
%Y Cf. A005651, A063834, A279375, A279790, A279791, A281113.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Mar 03 2018
%E a(12)-a(15) from _Alois P. Heinz_, Mar 03 2018
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