A275780 Number of set partitions of [n] into blocks with distinct element sums.

1, 1, 2, 4, 12, 43, 160, 668, 3098, 15465, 83100, 477651, 2914505, 18795814, 127790544, 911448954, 6808162094, 53067398065, 430956571977, 3636314065247, 31841519540324, 288664242344692, 2706949104147162, 26205222185730884, 261681461422075548, 2691088457402830312

Offset: 0

Author

Alois P. Heinz, Aug 08 2016

Keywords

• nonn

Examples

			a(3) = 4: 123, 13|2, 1|23, 1|2|3.
a(4) = 12: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 1|234, 1|23|4, 14|2|3, 1|24|3, 1|2|34, 1|2|3|4.
		

Links

• Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Crossrefs

Cf. A000110, A007837, A035470, A038041, A275781, A278339, A300335, A321469, A326512, A326513, A326519, A326535.

Programs

Mathematica

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Select[sps[Range[n]],UnsameQ@@Total/@#&]],{n,0,10}] (* Gus Wiseman, Jul 13 2019 *)

Formula

a(n) = A000110(n) - A275781(n).

Extensions

a(17)-a(25) from Christian Sievers, Aug 20 2024