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Search: id:A132993
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| A132993 |
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P partitions (A000041) weight symmetrical triangle of coefficients: t(n,m)=PartitionsP[n - m + 1]*PartitionsP[m + 1]. |
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+0
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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:
{1, 4, 10, 22, 43, 80, 141, 240, 397, 640, 1011}.
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REFERENCES
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Weisstein, Eric W. "Partition." http://mathworld.wolfram.com/Partition.html
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FORMULA
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t(n,m)=PartitionsP[n - m + 1]*PartitionsP[m + 1].
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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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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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Cf. A000041.
Sequence in context: A026350 A128282 A146985 this_sequence A106408 A143061 A096858
Adjacent sequences: A132990 A132991 A132992 this_sequence A132994 A132995 A132996
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Aug 27 2008
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