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A176289 Denominators of the rational sequence with e.g.f. (x/2)*(1+exp(-x))/(1-exp(-x)). 6
1, 1, 6, 1, 30, 1, 42, 1, 30, 1, 66, 1, 2730, 1, 6, 1, 510, 1, 798, 1, 330, 1, 138, 1, 2730, 1, 6, 1, 870, 1, 14322, 1, 510, 1, 6, 1, 1919190, 1, 6, 1, 13530, 1, 1806, 1, 690, 1, 282, 1, 46410, 1, 66, 1, 1590, 1, 798, 1, 870, 1, 354, 1, 56786730, 1, 6, 1, 510 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Denominator of the Bernoulli number B_n, except a(1)=1. A minor variant of the Bernoulli denominators A027642.

The series of fractions A164555(n)/A027642(n) =1/1, 1/2, 1/6, 0/1, -1/30,...

and the series of fractions A027641(n)/A027642(n) = B_n = 1/1, -1/2, 1/6, 0/1, -1/30.. differ only (by a sign) at n=1. The arithmetic mean of both series is 1/1, 0/1, 1/6, 0/1, -1/30,... , equal to the aerated series A000367(n)/A002445(n). The definition here provides the denominators of this series of arithmetic means.

LINKS

Table of n, a(n) for n=0..64.

FORMULA

a(2*n)= A002445(n), a(2*n+1)=1.

a(n) = A027642(n) for n!=1.

MAPLE

seq(denom((bernoulli(i, 0)+bernoulli(i, 1))/2), i=0..64); # Peter Luschny, Jun 17 2012

MATHEMATICA

Join[{1, 1}, Rest[Denominator[BernoulliB[Range[80]]]]] (* Harvey P. Dale, Jun 18 2012 *)

PROG

(PARI) apply(deniominator, Vec(serlaplace((x/2)*(1+exp(-x))/(1-exp(-x))))) \\ Charles R Greathouse IV, Sep 26 2017

CROSSREFS

Cf. A176327 (numerators), A141056.

Sequence in context: A147327 A145629 A193633 * A118933 A046212 A120105

Adjacent sequences:  A176286 A176287 A176288 * A176290 A176291 A176292

KEYWORD

nonn,frac

AUTHOR

Paul Curtz, Apr 14 2010

EXTENSIONS

More terms from Harvey P. Dale, May 03 2012

New name from Peter Luschny, Jun 18 2012

STATUS

approved

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Last modified August 20 20:34 EDT 2018. Contains 313927 sequences. (Running on oeis4.)