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A326513 Number of set partitions of {1..n} where each block has a different average. 8
1, 1, 2, 4, 12, 40, 154, 650, 3024, 15110, 81538, 468494, 2863340 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..12.

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

EXAMPLE

The a(1) = 1 through a(4) = 12 set partitions:

  {{1}}  {{1,2}}    {{1,2,3}}      {{1,2,3,4}}

         {{1},{2}}  {{1},{2,3}}    {{1},{2,3,4}}

                    {{1,2},{3}}    {{1,2},{3,4}}

                    {{1},{2},{3}}  {{1,2,3},{4}}

                                   {{1,2,4},{3}}

                                   {{1,3},{2,4}}

                                   {{1,3,4},{2}}

                                   {{1},{2},{3,4}}

                                   {{1},{2,3},{4}}

                                   {{1,2},{3},{4}}

                                   {{1,4},{2},{3}}

                                   {{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@@Mean/@#&]], {n, 0, 8}]

CROSSREFS

Cf. A000110, A007837, A035470, A038041, A275780, A326512, A326516, A326521, A326537.

Sequence in context: A074034 A268952 A215072 * A268953 A268954 A268955

Adjacent sequences:  A326510 A326511 A326512 * A326514 A326515 A326516

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 11 2019

EXTENSIONS

a(12) from Alois P. Heinz, Jul 12 2019

STATUS

approved

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Last modified February 22 15:26 EST 2020. Contains 332137 sequences. (Running on oeis4.)