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A275780 Number of set partitions of [n] into blocks with distinct element sums. 19
1, 1, 2, 4, 12, 43, 160, 668, 3098, 15465, 83100, 477651, 2914505, 18795814, 127790544, 911448954, 6808162094 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

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

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

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

Sequence in context: A096802 A139669 A179973 * A039301 A180205 A131529

Adjacent sequences:  A275777 A275778 A275779 * A275781 A275782 A275783

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Aug 08 2016

STATUS

approved

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Last modified February 20 12:34 EST 2020. Contains 332076 sequences. (Running on oeis4.)