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A322789 Irregular triangle read by rows where T(n,k) is the number of non-isomorphic uniform multiset partitions of a multiset with d = A027750(n,k) copies of each integer from 1 to n/d.

%I A322789 #13 Mar 05 2025 22:05:36
%S A322789 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 A322789 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 A322789 2,6,138,478,296,32,6,4,429,76,4,4,64,14,4
%N A322789 Irregular triangle read by rows where T(n,k) is the number of non-isomorphic uniform multiset partitions of a multiset with d = A027750(n,k) copies of each integer from 1 to n/d.
%C A322789 A multiset partition is uniform if all parts have the same size.
%H A322789 Andrew Howroyd, <a href="/A322789/b322789.txt">Table of n, a(n) for n = 1..338</a> (rows 1..75)
%e A322789 Triangle begins:
%e A322789   1
%e A322789   2  2
%e A322789   2  2
%e A322789   3  4  3
%e A322789   2  2
%e A322789   4  7  6  4
%e A322789   2  2
%e A322789   4 10  8  4
%e A322789   3  7  3
%e A322789   4 12  8  4
%e A322789 Non-isomorphic representatives of the multiset partitions counted under row 6:
%e A322789 {123456}           {112233}           {111222}           {111111}
%e A322789 {123}{456}         {112}{233}         {111}{222}         {111}{111}
%e A322789 {12}{34}{56}       {123}{123}         {112}{122}         {11}{11}{11}
%e A322789 {1}{2}{3}{4}{5}{6} {11}{22}{33}       {11}{12}{22}       {1}{1}{1}{1}{1}{1}
%e A322789                    {11}{23}{23}       {12}{12}{12}
%e A322789                    {12}{13}{23}       {1}{1}{1}{2}{2}{2}
%e A322789                    {1}{1}{2}{2}{3}{3}
%Y A322789 Row sums are A319056. First column is A000005.
%Y A322789 Cf. A001055, A005176, A027750, A056239, A072774, A100778, A295193, A306017, A306018, A319190, A319612, A322784, A322785, A322787, A322792.
%K A322789 nonn,tabf
%O A322789 1,2
%A A322789 _Gus Wiseman_, Dec 26 2018
%E A322789 Terms a(28) and beyond from _Andrew Howroyd_, Feb 03 2022
%E A322789 Name edited by _Peter Munn_, Mar 05 2025