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Search: id:A134133
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| A134133 |
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A certain partition array in Abramowitz-Stegun order (A-St order). |
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+0
7
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| 1, 2, 1, 6, 2, 1, 24, 6, 4, 2, 1, 120, 24, 12, 6, 4, 2, 1, 720, 120, 48, 36, 24, 12, 8, 6, 4, 2, 1, 5040, 720, 240, 144, 120, 48, 36, 24, 24, 12, 8, 6, 4, 2, 1, 40320, 5040, 1440, 720, 576, 720, 240, 144, 96, 72, 120, 48, 36, 24, 16, 24, 12, 8, 6, 4, 2, 1, 362880, 40320, 10080
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OFFSET
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1,2
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COMMENT
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The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].
Partition number array M_3(2)= A130561 divided by partition number array M_3 = M_3(1) = A036040.
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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].
W. Lang, First 10 rows and more.
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FORMULA
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a(n,k) = A130561(n,k)/A036040(n,k) (division of partition arrays M_3(2) by M_3).
a(n,k)= product(j!^e(n,k,j),j=1..n) with the exponent e(n,k,j) of j in the k-th partition of n in the A-St ordering of the partitions of n.
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EXAMPLE
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[1],[2,1],[6,2,1],[24,6,4,2,1],[120,24,12,6,4,2,1],...
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CROSSREFS
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With another ordering of the partitions this becomes A069123.
Cf. A134134 (triangle obtained by summing same m numbers).
Sequence in context: A110135 A114423 A069123 this_sequence A134134 A050457 A076891
Adjacent sequences: A134130 A134131 A134132 this_sequence A134134 A134135 A134136
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 12 2007
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