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Search: id:A145373
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| A145373 |
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Lower triangular array, called S1hat(-5), related to partition number array A145372. |
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+0
3
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| 1, 5, 1, 20, 5, 1, 60, 45, 5, 1, 120, 160, 45, 5, 1, 120, 820, 285, 45, 5, 1, 0, 1920, 1320, 285, 45, 5, 1, 0, 6600, 5420, 1945, 285, 45, 5, 1, 0, 9600, 23600, 7920, 1945, 285, 45, 5, 1, 0, 21600, 66600, 41100, 11045, 1945, 285, 45, 5, 1, 0, 14400, 189600, 151600, 53600, 11045
(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(-5):=A145372 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(-5). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first column is [1,5,20,60,120,120,0,0,0,...]= A008279(5,n-1), n>=1.
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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(-5;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(-5,n,1)= A008279(5,n-1) = [1,5,20,60,120,120,0,0,0,...], n>=1.
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EXAMPLE
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[1];[5,1];[20,5,1];[60,45,5,1];[120,160,45,5,1];...
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CROSSREFS
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A145374 (row sums).
Sequence in context: A066480 A136394 A145372 this_sequence A088577 A127561 A144879
Adjacent sequences: A145370 A145371 A145372 this_sequence A145374 A145375 A145376
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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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%N line: added two commas.First %C line: after 'entries'added 'belonging to partitions'.Last %C line: changed 'columns' into 'column'.First %Y line: erased the comma. - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 17 2008
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