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Search: id:A144886
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| A144886 |
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Lower triangular array called S1hat(4) related to partition number array A144885. |
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+0
5
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| 1, 4, 1, 20, 4, 1, 120, 36, 4, 1, 840, 200, 36, 4, 1, 6720, 1720, 264, 36, 4, 1, 60480, 12480, 2040, 264, 36, 4, 1, 604800, 118560, 16000, 2296, 264, 36, 4, 1, 6652800, 1081920, 149600, 17280, 2296, 264, 36, 4, 1, 79833600, 11793600, 1362240, 163680, 18304, 2296, 264
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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If in the partition array M31hat(4):=A144885 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(4). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first columns are A001715(n+2), A144888, A144889,...
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REFERENCES
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W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, preprint Oct 2008.
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LINKS
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W. Lang, First 10 rows of the array and more.
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FORMULA
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a(n,m)=sum(product(|S1(4;j,1)|^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S1(4,n,1)|= A049352(n,1) = A001715(n+2) = (n+2)!/3!.
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EXAMPLE
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[1];[4,1];[20,4,1];[120,36,4,1];[840,200,36,4,1];...
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CROSSREFS
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A144887 (row sums).
Sequence in context: A055139 A128041 A144885 this_sequence A117380 A167432 A078939
Adjacent sequences: A144883 A144884 A144885 this_sequence A144887 A144888 A144889
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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 09 2008
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