A322789 Irregular triangle read by rows where if d|n then T(n,d) is the number of non-isomorphic uniform multiset partitions of a multiset with d copies of each integer from 1 to n/d.

1, 2, 2, 2, 2, 3, 4, 3, 2, 2, 4, 7, 6, 4, 2, 2, 4, 10, 8, 4, 3, 7, 3, 4, 12, 8, 4, 2, 2, 6, 32, 35, 31, 18, 6, 2, 2, 4, 21, 10, 4, 4, 47, 29, 4, 5, 49, 72, 19, 5, 2, 2, 6, 81, 170, 71, 24, 6, 2, 2, 6, 138, 478, 296, 32, 6, 4, 429, 76, 4, 4, 64, 14, 4

Offset

1,2

Comments

A multiset partition is uniform if all parts have the same size.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..338 (rows 1..75)

Example

Triangle begins:
  1
  2  2
  2  2
  3  4  3
  2  2
  4  7  6  4
  2  2
  4 10  8  4
  3  7  3
  4 12  8  4
Non-isomorphic representatives of the multiset partitions counted under row 6:
{123456}           {112233}           {111222}           {111111}
{123}{456}         {112}{233}         {111}{222}         {111}{111}
{12}{34}{56}       {123}{123}         {112}{122}         {11}{11}{11}
{1}{2}{3}{4}{5}{6} {11}{22}{33}       {11}{12}{22}       {1}{1}{1}{1}{1}{1}
                   {11}{23}{23}       {12}{12}{12}
                   {12}{13}{23}       {1}{1}{1}{2}{2}{2}
                   {1}{1}{2}{2}{3}{3}

Crossrefs

Row sums are A319056. First column is A000005.

Cf. A001055, A005176, A056239, A072774, A100778, A295193, A306017, A306018, A319190, A319612, A322784, A322785, A322787, A322792.

Sequence in context: A171931 A221530 A262944 * A069904 A164978 A119789

Adjacent sequences: A322786 A322787 A322788 * A322790 A322791 A322792

Keyword

nonn,tabf

Author

Gus Wiseman, Dec 26 2018

Extensions

Terms a(28) and beyond from Andrew Howroyd, Feb 03 2022

Status

approved