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A085738
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Denominators in triangle formed from Bernoulli numbers.
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7
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1, 2, 2, 6, 3, 6, 1, 6, 6, 1, 30, 30, 15, 30, 30, 1, 30, 15, 15, 30, 1, 42, 42, 105, 105, 105, 42, 42, 1, 42, 21, 105, 105, 21, 42, 1, 30, 30, 105, 105, 105, 105, 105, 30, 30, 1, 30, 15, 105, 105, 105, 105, 15, 30, 1, 66, 66, 165, 165, 1155, 231, 1155, 165
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Triangle is determined by rules 0) the top number is 1; 1) each number is the sum of the two below it; 2) it is left-right symmetric; 3) the numbers in each of the border rows, after the first 3, are alternately 0.
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REFERENCES
| Lange, Fabien; and Grabisch, Michel; The interaction transform for functions on lattices. Discrete Math. 309 (2009), no. 12, 4037-4048. [From N. J. A. Sloane, Nov 26 2011]
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FORMULA
| T(n, 0) = (-1)^n*Bernoulli(n), T(n, k) = T(n-1, k-1) - T(n, k-1) for k=1..n.
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EXAMPLE
| Triangle begins
1
1/2, 1/2
1/6, 1/3, 1/6
0, 1/6, 1/6, 0
-1/30, 1/30, 2/15, 1/30, -1/30
0, -1/30, 1/15, 1/15, -1/30, 0
1/42, -1/42, -1/105, 8/105, -1/105, -1/42, 1/42
0, 1/42, -1/21, 4/105, 4/105, -1/21, 1/42, 0
-1/30, 1/30, -1/105, -4/105, 8/105, -4/105, -1/105, 1/30, -1/30
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CROSSREFS
| Cf. A085737. See A051714/A051715 for another triangle that generates the Bernoulli numbers.
Sequence in context: A128623 A182701 A174833 * A100641 A028421 A081745
Adjacent sequences: A085735 A085736 A085737 * A085739 A085740 A085741
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KEYWORD
| nonn,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) following a suggestion of J. H. Conway, Jul 23 2003
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EXTENSIONS
| Flipped a sign in the formula - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 02 2010
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