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Search: id:A134279
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| A134279 |
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A certain partition array in Abramowitz-Stegun order (A-St order), called M_3(6)/M_3. |
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3
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| 1, 6, 1, 66, 6, 1, 1056, 66, 36, 6, 1, 22176, 1056, 396, 66, 36, 6, 1, 576576, 22176, 6336, 4356, 1056, 396, 216, 66, 36, 6, 1, 17873856, 576576, 133056, 69696, 22176, 6336, 4356, 2376, 1056, 396, 216, 66, 36, 6, 1, 643458816, 17873856, 3459456, 1463616
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OFFSET
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1,2
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COMMENT
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Partition number array M_3(6) = A134278 with each entry divided by the corresponding one of the partition number array M_3 = M_3(1) = A036040; in short M_3(6)/M_3.
The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].
For the A-St order of partitions see the Abramowitz-Stegun reference given in A117506.
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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)= product(S2(6,j,1)^e(n,k,j),j=1..n) with S2(6,n,1) = A049385(n,1) = A008548(n) = (5*n-4)(!^5)(quintupel- or 5-factorials), and 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.
a(n,k) = A134278(n,k)/A036040(n,k) (division of partition arrays M_3(6) by M_3).
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EXAMPLE
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[1];[6,1];[66,6,1];[1056,66,36,6,1];[,22176,1056,396,66,36,6,1];...
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CROSSREFS
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Row sums give A134281 (also of triangle A134280).
Cf. A134274 (M_3(5)/M_3 partition array).
Sequence in context: A083837 A049213 A056218 this_sequence A134280 A134278 A049385
Adjacent sequences: A134276 A134277 A134278 this_sequence A134280 A134281 A134282
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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) Nov 13 2007
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