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Search: id:A144881
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| A144881 |
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Lower triangular array called S1hat(3) related to partition number array A144880. |
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+0
4
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| 1, 3, 1, 12, 3, 1, 60, 21, 3, 1, 360, 96, 21, 3, 1, 2520, 684, 123, 21, 3, 1, 20160, 4320, 792, 123, 21, 3, 1, 181440, 35640, 5292, 873, 123, 21, 3, 1, 1814400, 293760, 42768, 5616, 873, 123, 21, 3, 1, 19958400, 2881440, 348840, 45684, 5859, 873, 123, 21, 3, 1, 239500800
(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(3):=A144880 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(3). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first columns are A001710(n+1), A144883, A144884,...
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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(3;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(3,n,1)|= A046089(n,1) = A001710(n+1) = (n+1)!/2.
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EXAMPLE
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[1];[3,1];[12,3,1];[60,21,3,1];[360,96,21,3,1];...
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CROSSREFS
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A144882 (row sums).
Sequence in context: A118020 A124572 A144880 this_sequence A121420 A117375 A162995
Adjacent sequences: A144878 A144879 A144880 this_sequence A144882 A144883 A144884
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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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