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A051716
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Numerators of Bernoulli twin numbers C(n).
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12
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1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 5, -5, -691, 691, 7, -7, -3617, 3617, 43867, -43867, -174611, 174611, 854513, -854513, -236364091, 236364091, 8553103, -8553103, -23749461029, 23749461029, 8615841276005, -8615841276005, -7709321041217, 7709321041217, 2577687858367
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,11
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COMMENTS
| The Bernoulli twin numbers C(n) are defined by C(0) = 1, then C(2n) = B(2n)+B(2n-1), C(2n+1) = -B(2n+1)-B(2n), where B() are the Bernoulli numbers A027641/A027642. The definition is due to Paul Curtz.
Negatives of numerators of column 1 of table described in A051714/A051715.
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LINKS
| M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.
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EXAMPLE
| Sequence of C(n)'s begins: 1, -1/2, -1/3, -1/6, -1/30, 1/30, 1/42, -1/42, -1/30, 1/30, 5/66, -5/66, -691/2730, 691/2730, 7/6, -7/6, ...
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MAPLE
| C:=proc(n) if n=0 then RETURN(1); fi; if n mod 2 = 0 then RETURN(bernoulli(n)+bernoulli(n-1)); else RETURN(-bernoulli(n)-bernoulli(n-1)); fi; end;
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MATHEMATICA
| c[0] = 1; c[n_?EvenQ] := BernoulliB[n] + BernoulliB[n-1]; c[n_?OddQ] := -BernoulliB[n] - BernoulliB[n-1]; Table[ Numerator[c[n]], {n, 0, 34}] (* From Jean-François Alcover, Dec 19 2011 *)
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CROSSREFS
| Cf. A051717, A000367, A129825, A129826, A129724, A051714, A051715.
Sequence in context: A094463 A055928 A195567 * A102060 A102058 A078473
Adjacent sequences: A051713 A051714 A051715 * A051717 A051718 A051719
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KEYWORD
| sign,easy,nice,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 25 2008
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