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 A326512 Number of set partitions of {1..n} where every block has the same average. 8
 1, 1, 1, 2, 2, 5, 5, 18, 16, 75, 64, 405, 302, 2581, 1693, 19872 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS EXAMPLE The a(1) = 1 through a(7) = 18 set partitions:   {1}  {12}  {123}    {1234}    {12345}      {123456}      {1234567}              {13}{2}  {14}{23}  {1245}{3}    {1256}{34}    {123567}{4}                                 {135}{24}    {1346}{25}    {12467}{35}                                 {15}{234}    {16}{2345}    {1267}{345}                                 {15}{24}{3}  {16}{25}{34}  {13457}{26}                                                            {1357}{246}                                                            {1456}{237}                                                            {147}{2356}                                                            {156}{2347}                                                            {17}{23456}                                                            {1267}{35}{4}                                                            {1357}{26}{4}                                                            {147}{26}{35}                                                            {156}{237}{4}                                                            {17}{2356}{4}                                                            {17}{246}{35}                                                            {17}{26}{345}                                                            {17}{26}{35}{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]], SameQ@@Mean/@#&]], {n, 0, 8}] CROSSREFS Cf. A000110, A007837, A035470, A038041, A275780, A306017, A306021, A319169, A326513, A326515, A326520, A326536. Sequence in context: A245850 A245844 A083849 * A325983 A063501 A103892 Adjacent sequences:  A326509 A326510 A326511 * A326513 A326514 A326515 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 11 2019 EXTENSIONS a(12)-a(15) from Alois P. Heinz, Jul 12 2019 STATUS approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)