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A131136 Denominator of (exponential) expansion of log((x/2-1)/(x-1)).

%I A131136 #17 Mar 17 2019 02:04:23
%S A131136 1,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,
%T A131136 32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,
%U A131136 16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16
%N A131136 Denominator of (exponential) expansion of log((x/2-1)/(x-1)).
%C A131136 a(n+1) = 2^A063787(n). a(n+1) = A001316(n)/2. - _Stephen Crowley_, Aug 25 2008
%C A131136 Also, 1 followed by A117973. - _Omar E. Pol_, Dec 11 2010
%F A131136 a(n) = 0^n + n + Sum_{k=0..n-1} (-1)^(1 + binomial(n-1,k)). - _Stephen Crowley_, Aug 25 2008
%e A131136 From _Omar E. Pol_, Jun 14 2009, Dec 11 2010: (Start)
%e A131136 May be written as a triangle by using the Crowley formula with A063787:
%e A131136 .1;
%e A131136 .2;
%e A131136 .4,4;
%e A131136 .8,4,8,8;
%e A131136 .16,4,8,8,16,8,16,16;
%e A131136 .32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32;
%e A131136 .64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,...
%e A131136 Also
%e A131136 1,
%e A131136 2,
%e A131136 4,
%e A131136 4,8,
%e A131136 4,8,8,16,
%e A131136 4,8,8,16,8,16,16,32,
%e A131136 4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,
%e A131136 4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,...
%e A131136 (End)
%p A131136 a(n)=abs(op(1, numer(expand(Zeta(2n)/Zeta(1-2n))))) # _Stephen Crowley_, Aug 25 2008
%t A131136 With[{nn=80},Denominator[CoefficientList[Series[Log[(x/2-1)/(x-1)],{x,0,nn}],x] Range[0,nn]!]] (* _Harvey P. Dale_, Apr 28 2016 *)
%Y A131136 Cf. A001316, A131135.
%Y A131136 Cf. A063787.
%Y A131136 Cf. A000079, A117973. - _Omar E. Pol_, Jun 14 2009, Dec 11 2010
%K A131136 nonn
%O A131136 0,2
%A A131136 _Paul Barry_, Jun 17 2007