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A132993
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Triangle t(n,m) = P(n-m+1) * P(m+1) read by rows, 0<=m<=n, where P=A000041 are the partition numbers.
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1
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1, 2, 2, 3, 4, 3, 5, 6, 6, 5, 7, 10, 9, 10, 7, 11, 14, 15, 15, 14, 11, 15, 22, 21, 25, 21, 22, 15, 22, 30, 33, 35, 35, 33, 30, 22, 30, 44, 45, 55, 49, 55, 45, 44, 30, 42, 60, 66, 75, 77, 77, 75, 66, 60, 42, 56, 84, 90, 110, 105, 121, 105, 110, 90, 84, 56
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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EXAMPLE
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1;
2, 2;
3, 4, 3;
5, 6, 6, 5;
7, 10, 9, 10, 7;
11, 14, 15, 15, 14, 11;
15, 22, 21, 25, 21, 22, 15;
22, 30, 33, 35, 35, 33, 30, 22;
30, 44, 45, 55, 49, 55, 45, 44, 30;
42, 60, 66, 75, 77, 77, 75, 66, 60, 42;
56, 84, 90, 110, 105, 121, 105, 110, 90, 84, 56;
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MAPLE
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combinat[numbpart](n-m+1)*combinat[numbpart](m+1) ;
end proc:
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MATHEMATICA
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<< DiscreteMath`Combinatorica`; << DiscreteMath`IntegerPartitions`; Clear[t, n, m]; t[n_, m_] = PartitionsP[n - m + 1]*PartitionsP[m + 1]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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