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

Author

Paul Curtz, Apr 14 2010

Keywords

• nonn
• frac

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

Crossrefs

Cf. A027641, A027642, A164555, A176327 (numerators), A141056.

Programs

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 *)

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

Formula

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

a(n) = A027642(n) for n <> 1.

Extensions

More terms from Harvey P. Dale, May 03 2012

New name from Peter Luschny, Jun 18 2012