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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.
3
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
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Dec 26 2018
EXTENSIONS
Terms a(28) and beyond from Andrew Howroyd, Feb 03 2022
STATUS
approved