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Search: id:A145357
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| A145357 |
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Lower triangular array, called S1hat(6), related to partition number array A145356. |
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+0
5
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| 1, 6, 1, 42, 6, 1, 336, 78, 6, 1, 3024, 588, 78, 6, 1, 30240, 6804, 804, 78, 6, 1, 332640, 62496, 8316, 804, 78, 6, 1, 3991680, 753984, 85176, 9612, 804, 78, 6, 1, 51891840, 8273664, 1021608, 94248, 9612, 804, 78, 6, 1, 726485760, 109118016, 11394432, 1157688, 102024
(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(6):=A145356 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(6). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first columns are A001725(n+4), A145359, A145360,...
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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(6;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(6,n,1)|= A049374(n,1) = A001725(n+4) = (n+4)!/5!.
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EXAMPLE
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[1];[6,1];[42,6,1];[336,78,6,1];[3024,588,78,6,1];...
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CROSSREFS
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A145358(row sums).
Sequence in context: A145927 A113365 A145356 this_sequence A035529 A135893 A051338
Adjacent sequences: A145354 A145355 A145356 this_sequence A145358 A145359 A145360
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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 17 2008
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EXTENSIONS
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In %N: added two commas.In the first %C line: added after entries: 'belonging to partitions'. - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 17 2008
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