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Search: id:A134274
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| A134274 |
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A certain partition array in Abramowitz-Stegun order (A-St order), called M_3(5)/M_3. |
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4
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| 1, 5, 1, 45, 5, 1, 585, 45, 25, 5, 1, 9945, 585, 225, 45, 25, 5, 1, 208845, 9945, 2925, 2025, 585, 225, 125, 45, 25, 5, 1, 5221125, 208845, 49725, 26325, 9945, 2925, 2025, 1125, 585, 225, 125, 45, 25, 5, 1, 151412625, 5221125, 1044225, 447525, 342225
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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(5) = A134273 with each entry divided by the corresponding one of the partition number array M_3 = M_3(1) = A036040; in short M_3(5)/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(5,j,1)^e(n,k,j),j=1..n) with S2(5,n,1) = A049029(n,1) = A007696(n) = (4*n-3)(!^4)(quadrupel- or 4-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) = A134273(n,k)/A036040(n,k) (division of partition arrays M_3(5) by M_3).
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EXAMPLE
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[1]; [5,1]; [45,5,1]; [585,45,25,5,1]; [9945,585,225,45,25,5,1];...
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CROSSREFS
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Row sums A134276 (also of triangle A134275).
Cf. A134150 (M_3(4)/M_3 array).
Sequence in context: A039817 A000321 A039922 this_sequence A134275 A114154 A134273
Adjacent sequences: A134271 A134272 A134273 this_sequence A134275 A134276 A134277
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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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