A322789 - OEIS

%I #9 Feb 03 2022 16:43:42

%S 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,

%T 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,

%U 2,6,138,478,296,32,6,4,429,76,4,4,64,14,4

%N 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.

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

%H Andrew Howroyd, <a href="/A322789/b322789.txt">Table of n, a(n) for n = 1..338</a> (rows 1..75)

%e Triangle begins:

%e   1

%e   2  2

%e   2  2

%e   3  4  3

%e   2  2

%e   4  7  6  4

%e   2  2

%e   4 10  8  4

%e   3  7  3

%e   4 12  8  4

%e Non-isomorphic representatives of the multiset partitions counted under row 6:

%e {123456}           {112233}           {111222}           {111111}

%e {123}{456}         {112}{233}         {111}{222}         {111}{111}

%e {12}{34}{56}       {123}{123}         {112}{122}         {11}{11}{11}

%e {1}{2}{3}{4}{5}{6} {11}{22}{33}       {11}{12}{22}       {1}{1}{1}{1}{1}{1}

%e                    {11}{23}{23}       {12}{12}{12}

%e                    {12}{13}{23}       {1}{1}{1}{2}{2}{2}

%e                    {1}{1}{2}{2}{3}{3}

%Y Row sums are A319056. First column is A000005.

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

%K nonn,tabf

%O 1,2

%A _Gus Wiseman_, Dec 26 2018

%E Terms a(28) and beyond from _Andrew Howroyd_, Feb 03 2022