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A134284
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A certain partition array in Abramowitz-Stegun order (A-St order), called M_0(3)/M_0.
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2
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1, 3, 1, 10, 3, 1, 35, 10, 9, 3, 1, 126, 35, 30, 10, 9, 3, 1, 462, 126, 105, 100, 35, 30, 27, 10, 9, 3, 1, 1716, 462, 378, 350, 126, 105, 100, 90, 35, 30, 27, 10, 9, 3, 1, 6435, 1716, 1386, 1260, 1225, 462, 378, 350, 315, 300, 126, 105, 100, 90, 81, 35, 30, 27, 10, 9, 3, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
Partition number array M_0(3)= A134283 with each entry divided by the corresponding one of the partition number array M_0 = M_0(2) = A048996; in short M_0(3)/M_0.
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
W. Lang, First 10 rows and more.
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FORMULA
| a(n,k)= product(s2(3,j,1)^e(n,k,j),j=1..n) with s2(3,n,1) = A035324(n,1) = A001700(n-1) = binomial(2*n-1,n) 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) = A134283(n,k)/A048996(n,k) (division of partition arrays M_0(3) by M_0).
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EXAMPLE
| [1];[3,1];[10,3,1];[35,10,9,3,1];[126,35,30,10,9,3,1];...
a(4,3)=9=3^2 because (2^2) is the k=4 partition of n=4 in A-St order and s2(3,2,1)=3.
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CROSSREFS
| Cf. A134826 (row sums coinciding with those of triangle A134285).
Sequence in context: A102430 A135573 A126953 * A134285 A141811 A126954
Adjacent sequences: A134281 A134282 A134283 * A134285 A134286 A134287
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 13 2007
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