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A322787
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Irregular triangle read by rows where if d|n then T(n,d) is the number of non-isomorphic multiset partitions of a multiset with d copies of each integer from 1 to n/d.
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3
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1, 2, 2, 3, 3, 5, 7, 5, 7, 7, 11, 23, 21, 11, 15, 15, 22, 79, 66, 22, 30, 162, 30, 42, 274, 192, 42, 56, 56, 77, 1003, 1636, 1338, 565, 77, 101, 101, 135, 3763, 1579, 135, 176, 19977, 10585, 176, 231, 14723, 43686, 4348, 231, 297, 297, 385, 59663, 298416, 82694, 11582, 385
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Triangle begins:
1
2 2
3 3
5 7 5
7 7
11 23 21 11
15 15
22 79 66 22
30 162 30
42 274 192 42
Non-isomorphic representatives of the multiset partitions counted under row 6:
{123456} {112233} {111222} {111111}
{1}{23456} {1}{12233} {1}{11222} {1}{11111}
{12}{3456} {11}{2233} {11}{1222} {11}{1111}
{123}{456} {112}{233} {111}{222} {111}{111}
{1}{2}{3456} {12}{1233} {112}{122} {1}{1}{1111}
{1}{23}{456} {123}{123} {12}{1122} {1}{11}{111}
{12}{34}{56} {1}{1}{2233} {1}{1}{1222} {11}{11}{11}
{1}{2}{3}{456} {1}{12}{233} {1}{11}{222} {1}{1}{1}{111}
{1}{2}{34}{56} {11}{22}{33} {11}{12}{22} {1}{1}{11}{11}
{1}{2}{3}{4}{56} {11}{23}{23} {1}{12}{122} {1}{1}{1}{1}{11}
{1}{2}{3}{4}{5}{6} {1}{2}{1233} {1}{2}{1122} {1}{1}{1}{1}{1}{1}
{12}{13}{23} {12}{12}{12}
{1}{23}{123} {2}{11}{122}
{2}{11}{233} {1}{1}{1}{222}
{1}{1}{2}{233} {1}{1}{12}{22}
{1}{1}{22}{33} {1}{1}{2}{122}
{1}{1}{23}{23} {1}{2}{11}{22}
{1}{2}{12}{33} {1}{2}{12}{12}
{1}{2}{13}{23} {1}{1}{1}{2}{22}
{1}{2}{3}{123} {1}{1}{2}{2}{12}
{1}{1}{2}{2}{33} {1}{1}{1}{2}{2}{2}
{1}{1}{2}{3}{23}
{1}{1}{2}{2}{3}{3}
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PROG
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(PARI) \\ See A318951 for RowSumMats
row(n)={my(d=divisors(n)); vector(#d, i, RowSumMats(n/d[i], n, d[i]))}
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CROSSREFS
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Cf. A001055, A005176, A056239, A072774, A100778, A295193, A306018, A318951, A319190, A319612, A322784, A322785, A322788, A322792.
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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