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%I #16 Sep 08 2022 08:45:14
%S 1,108,1296,326592,15116544,665127936,28298170368,235092492288,
%T 47958868426752,1929639176699904,10968475320188928,
%U 3027299188372144128,4738381338321616896,4605706660848611622912,178087324219479649419264,6853291511342734094893056
%N Denominators of upper bounds for Lagrange-remainder in Taylor's expansion of log((1+x)/(1-x)) multiplied by 6/5.
%C An upper bound for the Lagrange-remainder in the expansion of log((1+x)/(1-x)) for x=1/3, i.e., for log(2), is R(2*n):=(1/2^(2*n+1) + 1/3^(2*n+1))/(2*n+1).
%D M. Barner and F. Flohr, Analysis I, de Gruyter, 5te Auflage, 2000; p. 293.
%H W. Lang, <a href="/A096952/a096952.txt">More comments</a>.
%F a(n)=denominator(A(n)), where A(n):=(6/5)*(1/2^(2*n+1) + 1/3^(2*n+1))/(2*n+1) = A096951(n)/((2*n+1)*6^(2*n)).
%e n=4: R(2*4)=(5/6)* A096952(4)/a(4) = (5/6)*4039/15116544 = 20195/90699264 = 0.0002226589..., therefore log(2)-2*sum(((1/3)^(2*k-1))/(2*k-1),k=1..4) < 0.0002226589... In fact, the partial sum is 0.0000124233...
%o (PARI) vector(30, n, n--; denominator((6/5)*(1/2^(2*n+1) + 1/3^(2*n+1))/(2*n+1))) \\ _Michel Marcus_, Jul 06 2015
%o (Magma) [Denominator((6/5)*(1/2^(2*n+1) + 1/3^(2*n+1))/(2*n+1)): n in [0..20]]; // _Vincenzo Librandi_, Jul 06 2015
%Y Numerators are given in A096952.
%K nonn,easy,frac
%O 0,2
%A _Wolfdieter Lang_, Jul 16 2004
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