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A051716 Numerators of Bernoulli twin numbers C(n). 20
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; text; internal format)
OFFSET

0,11

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.

LINKS

Table of n, a(n) for n=0..34.

M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.

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, ...

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;

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}] (* Jean-Fran├žois Alcover, Dec 19 2011 *)

CROSSREFS

Cf. A051717, A000367, A129825, A129826, A129724, A051714, A051715.

Sequence in context: A055928 A213145 A195567 * A226260 A102060 A102058

Adjacent sequences:  A051713 A051714 A051715 * A051717 A051718 A051719

KEYWORD

sign,easy,nice,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Dec 08 1999

Edited by N. J. A. Sloane, May 25 2008

STATUS

approved

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Last modified December 3 21:14 EST 2016. Contains 278745 sequences.