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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

Table of n, a(n) for n=1..37.

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.)