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Search: id:A134134
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| A134134 |
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Triangle of numbers obtained from the partition array A134133. |
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+0
8
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| 1, 2, 1, 6, 2, 1, 24, 10, 2, 1, 120, 36, 10, 2, 1, 720, 204, 44, 10, 2, 1, 5040, 1104, 228, 44, 10, 2, 1, 40320, 7776, 1272, 244, 44, 10, 2, 1, 362880, 57600, 8760, 1320, 244, 44, 10, 2, 1, 3628800, 505440, 63936, 9096, 1352, 244, 44, 10, 2, 1
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.
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LINKS
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W. Lang, First 10 rows and more.
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FORMULA
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a(n,m)=sum(product(j!^e(n,m,k,j),j=1..n),k=1..p(n,m)) if n>=m>=1, else 0, with p(n,m)=A008284(n,m), the number of m parts partitions of n, and e(n,m,k,j) is the exponent of j in the k-th m part partition of n.
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EXAMPLE
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[1];[2,1];[6,2,1];[24,10,2,1];[120,36,10,2,1];...
a(4,2)=10 from the sum over the numbers related to the partitions (1,3) and (2^2), namely
1!^1*3!^1 + 2!^2 = 6+4 = 10.
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CROSSREFS
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Row sums A077365. Alternating row sums A134135.
Adjacent sequences: A134131 A134132 A134133 this_sequence A134135 A134136 A134137
Sequence in context: A114423 A069123 A134133 this_sequence A050457 A076891 A071883
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KEYWORD
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nonn,easy,tabl
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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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