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A119271
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Triangle: number of exactly (m-1)-dimensional partitions of n, for n >= 1, m >= 0.
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3
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1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 5, 6, 1, 0, 1, 9, 18, 10, 1, 0, 1, 13, 44, 49, 15, 1, 0, 1, 20, 97, 172, 110, 21, 1, 0, 1, 28, 195, 512, 550, 216, 28, 1, 0, 1, 40, 377, 1370, 2195, 1486, 385, 36, 1, 0, 1, 54, 694, 3396, 7603, 7886, 3514, 638, 45, 1, 0, 1, 75, 1251, 7968
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OFFSET
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1,9
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COMMENTS
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The partition of 1 is considered to be dimension -1 by convention.
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LINKS
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Suresh Govindarajan, Partitions Generator (gives partitions of integers <= 25 in any dimension using this triangle).
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FORMULA
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a(n,m) = A096806(n,m-1)-a(n,m-1). Binomial transform of n-th row lists the (m-1) dimensional partitions of n.
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EXAMPLE
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Table starts:
1,
0,1,
0,1,1,
0,1,3,1,
0,1,5,6,1,
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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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