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Search: id:A134283
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| A134283 |
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A certain partition array in Abramowitz-Stegun (A-St)order, called M_0(3). |
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3
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| 1, 3, 1, 10, 6, 1, 35, 20, 9, 9, 1, 126, 70, 60, 30, 27, 12, 1, 462, 252, 210, 100, 105, 180, 27, 40, 54, 15, 1, 1716, 924, 756, 700, 378, 630, 300, 270, 140, 360, 108, 50, 90, 18, 1, 6435, 3432, 2772, 2520, 1225, 1386, 2268, 2100, 945, 900, 504, 1260, 600, 1080, 81
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For the A-St order of partitions see the Abramowitz-Stegun reference given in A117506.
Partition number array M_0(3); the k=3 member in the family of a generalization of the multinomial number arrays M_0 = M_0(2) = A048996.
The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].
The s2(3,n,m):=A035324(n,m) numbers (generalized Pascal triangle) are obtained by summing in row n all numbers with the same part number m. In the same manner the s2(2,n,m)= binomial(n-1,m-1)= A007318(n-1,m-1) numbers are obtained from the partition array M_0= A048996.
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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)= m!*product((s2(3,j,1)^e(n,k,j))/e(n,k,j)!,j=1..n) with s2(3,n,1)= A035324(n,1) = A001700(n-1), and 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. Exponents 0 can be omitted due to 0!=1.
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EXAMPLE
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[1];[3,1];[10,6,1];[35,20,9,9,1];[126,70,60,30,27,12,1];...
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CROSSREFS
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Cf. A049027 (row sums, also of triangle A035324).
Sequence in context: A113187 A057967 A132964 this_sequence A035324 A091965 A107056
Adjacent sequences: A134280 A134281 A134282 this_sequence A134284 A134285 A134286
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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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