A176289 Denominators of the rational sequence with e.g.f. (x/2)*(1+exp(-x))/(1-exp(-x)).

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

Offset

0,3

Comments

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

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

and the sequence 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 sequences is 1/1, 0/1, 1/6, 0/1, -1/30, ..., equal to the aerated sequence A000367(n)/A002445(n). The definition here provides the denominators of this sequence of arithmetic means.

Links

Antti Karttunen, Table of n, a(n) for n = 0..4096

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
(PARI) A176289(n) = if(1==n, n, denominator(bernfrac(n))); \\ Antti Karttunen, Dec 19 2018

Crossrefs

Cf. A027641, A027642, A164555, 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