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Search: id:A085738
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| A085738 |
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Denominators in triangle formed from Bernoulli numbers. |
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+0
2
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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
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OFFSET
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0,2
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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. A085737. See A051714/A051715 for another triangle that generates the Bernoulli numbers.
Sequence in context: A100346 A130478 A128623 this_sequence A100641 A028421 A081745
Adjacent sequences: A085735 A085736 A085737 this_sequence A085739 A085740 A085741
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KEYWORD
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nonn,frac
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AUTHOR
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njas following a suggestion of J. H. Conway, Jul 23 2003
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