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Search: id:A106828
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| A106828 |
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Triangle T(n,k) read by rows: associated Stirling numbers of first kind (n >= 0 and, for n>=2, 0 <= k <= floor(n/2)). |
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+0
2
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| 1, 0, 0, 0, 1, 0, 2, 0, 6, 3, 0, 24, 20, 0, 120, 130, 15, 0, 720, 924, 210, 0, 5040, 7308, 2380, 105, 0, 40320, 64224, 26432, 2520, 0, 362880, 623376, 303660, 44100, 945, 0, 3628800, 6636960, 3678840, 705320, 34650, 0, 39916800, 76998240, 47324376, 11098780, 866250, 10395
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Another version of the triangle in A008306, which see for formulae, references etc.
A signed version of this triangle is given by the exponential Riordan array [1, log(1+t)-t]. Its row sums are (-1)^n*(1-n). Another version is [1, log(1-t)+t], whose row sums are 1-n. - Paul Barry (pbarry(AT)wit.ie), May 10 2008
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 75.
Feng-Zhen Zhao, Some Properties of Associated Stirling Numbers, Journal of Integer Sequences, Article 08.1.7, 2008
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EXAMPLE
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Rows 0 though 7 are:
1
0 0
0 1
0 2
0 6 3
0 24 20
0 120 130 15
0 720 924 210
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CROSSREFS
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See A008306 for more information.
Sequence in context: A049257 A054877 A095834 this_sequence A055302 A055349 A161174
Adjacent sequences: A106825 A106826 A106827 this_sequence A106829 A106830 A106831
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KEYWORD
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tabf,nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 22 2005
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