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 A322788 Irregular triangle read by rows where if d|n then T(n,d) is the number of uniform multiset partitions of a multiset with d copies of each integer from 1 to n/d. 3
 1, 2, 2, 2, 2, 5, 4, 3, 2, 2, 27, 11, 6, 4, 2, 2, 142, 29, 8, 4, 282, 12, 3, 1073, 101, 8, 4, 2, 2, 32034, 1581, 234, 75, 20, 6, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A multiset partition is uniform if all parts have the same size. LINKS FORMULA T(n,d) = A322794(A002110(n/d)^d). EXAMPLE Triangle begins:      1      2    2      2    2      5    4    3      2    2     27   11    6    4      2    2    142   29    8    4    282   12    3   1073  101    8    4 The multiset partitions counted under row 6:   {123456}          {112233}          {111222}          {111111}   {123}{456}        {112}{233}        {111}{222}        {111}{111}   {124}{356}        {113}{223}        {112}{122}        {11}{11}{11}   {125}{346}        {122}{133}        {11}{12}{22}      {1}{1}{1}{1}{1}{1}   {126}{345}        {123}{123}        {12}{12}{12}   {134}{256}        {11}{22}{33}      {1}{1}{1}{2}{2}{2}   {135}{246}        {11}{23}{23}   {136}{245}        {12}{12}{33}   {145}{236}        {12}{13}{23}   {146}{235}        {13}{13}{22}   {156}{234}        {1}{1}{2}{2}{3}{3}   {12}{34}{56}   {12}{35}{46}   {12}{36}{45}   {13}{24}{56}   {13}{25}{46}   {13}{26}{45}   {14}{23}{56}   {14}{25}{36}   {14}{26}{35}   {15}{23}{46}   {15}{24}{36}   {15}{26}{34}   {16}{23}{45}   {16}{24}{35}   {16}{25}{34}   {1}{2}{3}{4}{5}{6} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; Table[Length[Select[mps[Join@@Table[Range[n/d], {d}]], SameQ@@Length/@#&]], {n, 10}, {d, Divisors[n]}] CROSSREFS Row sums are A322785. First column is A038041. Cf. A001055, A005176, A056239, A072774, A100778, A295193, A306017, A319190, A319612, A322784, A322785, A322786, A322789, A322792. Sequence in context: A324516 A181058 A301452 * A177333 A118486 A288026 Adjacent sequences:  A322785 A322786 A322787 * A322789 A322790 A322791 KEYWORD nonn,tabf,more AUTHOR Gus Wiseman, Dec 26 2018 EXTENSIONS More terms from Alois P. Heinz, Jan 30 2019 STATUS approved

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Last modified December 10 15:09 EST 2019. Contains 329896 sequences. (Running on oeis4.)