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Search: id:A145364
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| A145364 |
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Lower triangular array, called S1hat(-2), related to partition number array A145363. |
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+0
4
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| 1, 2, 1, 2, 2, 1, 0, 6, 2, 1, 0, 4, 6, 2, 1, 0, 4, 12, 6, 2, 1, 0, 0, 12, 12, 6, 2, 1, 0, 0, 8, 28, 12, 6, 2, 1, 0, 0, 8, 24, 28, 12, 6, 2, 1, 0, 0, 0, 24, 56, 28, 12, 6, 2, 1, 0, 0, 0, 16, 56, 56, 28, 12, 6, 2, 1, 0, 0, 0, 16, 48, 120, 56, 28, 12, 6, 2, 1, 0, 0, 0, 0, 48, 112, 120, 56, 28, 12, 6, 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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If in the partition array M31hat(-2):=A145363 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(-2). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first column is [1,2,2,0,0,0,...]= A008279(2,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(-2;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(-2,n,1)= A008279(2,n-1) = [1,2,2,0,0,0,...], n>=1.
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EXAMPLE
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[1];[2,1];[2,2,1];[0,6,2,1];[0,4,6,2,1];...
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CROSSREFS
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A145365 (row sums).
Sequence in context: A004570 A145363 A071429 this_sequence A156263 A109672 A025917
Adjacent sequences: A145361 A145362 A145363 this_sequence A145365 A145366 A145367
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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 the %N line: added two commas.In the first %C line: added after 'entries': 'belonging to partitions'In the second %C line: changed 'columns' into 'column'. - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 17 2008
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