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Search: id:A085737
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| A085737 |
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Numerators in triangle formed from Bernoulli numbers. |
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+0
7
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| 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, -1, 1, 2, 1, -1, 0, -1, 1, 1, -1, 0, 1, -1, -1, 8, -1, -1, 1, 0, 1, -1, 4, 4, -1, 1, 0, -1, 1, -1, -4, 8, -4, -1, 1, -1, 0, -1, 1, -8, 4, 4, -8, 1, -1, 0, 5, -5, 7, 4, -116, 32, -116, 4, 7, -5, 5, 0, 5, -5, 32, -28, 16, 16, -28, 32, -5, 5, 0
(list; graph; listen)
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OFFSET
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0,13
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COMMENT
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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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FORMULA
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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
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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
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Cf. A085738. See A051714/A051715 for another triangle that generates the Bernoulli numbers.
Sequence in context: A037800 A144411 A138253 this_sequence A005090 A073490 A135341
Adjacent sequences: A085734 A085735 A085736 this_sequence A085738 A085739 A085740
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), following a suggestion of J. H. Conway, Jul 23 2003
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