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 A326513 Number of set partitions of {1..n} where each block has a different average. 16
 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 25 13:12 EST 2024. Contains 370330 sequences. (Running on oeis4.)