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%I #33 Jul 25 2021 10:52:19
%S 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,
%T 1,6,1,870,1,14322,1,510,1,6,1,1919190,1,6,1,13530,1,1806,1,690,1,282,
%U 1,46410,1,66,1,1590,1,798,1,870,1,354,1,56786730,1,6,1,510
%N Denominators of the rational sequence with e.g.f. (x/2)*(1+exp(-x))/(1-exp(-x)).
%C Denominator of the Bernoulli number B_n, except a(1)=1. A minor variant of the Bernoulli denominators A027642.
%C The sequence of fractions A164555(n)/A027642(n) = 1/1, 1/2, 1/6, 0/1, -1/30, ...
%C 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.
%H Antti Karttunen, <a href="/A176289/b176289.txt">Table of n, a(n) for n = 0..4096</a>
%F a(2*n) = A002445(n), a(2*n+1)=1.
%F a(n) = A027642(n) for n <> 1.
%p seq(denom((bernoulli(i,0)+bernoulli(i,1))/2),i=0..64); # _Peter Luschny_, Jun 17 2012
%t Join[{1,1},Rest[Denominator[BernoulliB[Range[80]]]]] (* _Harvey P. Dale_, Jun 18 2012 *)
%o (PARI) apply(deniominator, Vec(serlaplace((x/2)*(1+exp(-x))/(1-exp(-x))))) \\ _Charles R Greathouse IV_, Sep 26 2017
%o (PARI) A176289(n) = if(1==n,n,denominator(bernfrac(n))); \\ _Antti Karttunen_, Dec 19 2018
%Y Cf. A027641, A027642, A164555, A176327 (numerators), A141056.
%K nonn,frac
%O 0,3
%A _Paul Curtz_, Apr 14 2010
%E More terms from _Harvey P. Dale_, May 03 2012
%E New name from _Peter Luschny_, Jun 18 2012
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