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0, 1, 5, 1, 31, 1, 41, 1, 31, 1, 61, 1, 3421, 1, -1, 1, 4127, 1, -43069, 1, 174941, 1, -854375, 1, 236366821, 1, -8553097, 1, 23749461899, 1, -8615841261683, 1, 7709321041727, 1, -2577687858361, 1, 26315271553055396563, 1, -2929993913841553, 1
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OFFSET
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0,3
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COMMENTS
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If n != 1, also the numerator of 1 - Bernoulli(n). The denominators are in A027642.
(There are no common factors to be canceled in the fractions.)
The numerators of 1 - Bernoulli(n) start 0, 3, 5,1, 31, ... and differ only at n=1 from this sequence.
E.g.f. for the rationals r(n) = a(n)/A027642(n) = 1 - A164555(n)/A027642(n): exp(x)*(1 - x/(exp(x) - 1)). - Wolfdieter Lang, Aug 07 2017
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LINKS
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Table of n, a(n) for n=0..39.
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FORMULA
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|a(2n)| = A162173(n+1).
a(2n+1) = 1.
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EXAMPLE
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The rationals r(n) begin: 0, 1/2, 5/6, 1, 31/30, 1, 41/42, 1, 31/30, 1, 61/66, 1, 3421/2730, 1, -1/6, 1, 4127/510, 1, -43069/798, 1, ... - Wolfdieter Lang, Aug 07 2017
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MAPLE
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A165226 := proc(n) if n = 1 then 1+bernoulli(n) ; else 1-bernoulli(n) ; end if; numer(%) ; end proc: # R. J. Mathar, Jan 16 2011
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CROSSREFS
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Cf. A162173, A164555, A027642.
Sequence in context: A062140 A144355 A049353 * A027759 A197654 A296043
Adjacent sequences: A165223 A165224 A165225 * A165227 A165228 A165229
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KEYWORD
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frac,easy,sign
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AUTHOR
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Paul Curtz, Sep 09 2009
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STATUS
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approved
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