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Search: id:A069123
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| A069123 |
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Triangle formed as follows. For n-th row, n = 0, 1, ..., record the A000041(n) partitions of n; for each partition, write down number of ways to arrange the parts. |
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+0
3
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| 1, 1, 2, 1, 6, 2, 1, 24, 6, 4, 2, 1, 120, 24, 12, 6, 4, 2, 1, 720, 120, 48, 24, 36, 12, 6, 8, 4, 2, 1, 5040, 720, 240, 120, 144, 48, 24, 36, 24, 12, 6, 8, 4, 2, 1, 40320, 5040, 1440, 720, 720, 240, 120, 576, 144, 96, 48, 24, 72, 36, 24, 12, 6, 16, 8, 4, 2, 1
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
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FORMULA
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[<n[k]>]!=prod_k(n[k]!), or equivalently, [<n[k]^m[k]>]!=prod_k(n[k]!^m[k]).
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EXAMPLE
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This is a function of the individual partitions of an integer. For n = 0 to 5 the terms are (1), (1), (2,1), (6,2,1), (24,6,4,2,1). The partitions are ordered with the largest part sizes first, so the row 4 indices are [4], [3,1], [2,2], [2,1,1], and [1,1,1,1].
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CROSSREFS
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Cf. A000142.
Using Abramowitz-Stegun ordering of partitions this becomes array A134133.
Sequence in context: A106187 A110135 A114423 this_sequence A134133 A134134 A050457
Adjacent sequences: A069120 A069121 A069122 this_sequence A069124 A069125 A069126
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 07 2002
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