Sorry, with G11 looming, I had not time to make it shorter: (1/(36*n*(1 + n)))*(-3 + 3*n*(-3*n*(4 + n*(7 + 2*n)) + 4*n*z1 + 4*(1 + z1)) + n*(4*ArcCoth[3*n] - 18*Log[n] + 84*Log[1 + n] - 69*Log[2 + n] + 4*Log[-1 + 3*n] - 3*Log[-1 + 9*n^2] + Log[(6144*Pi^6)/ Gamma[1/6]^12] + n*(15*Log[2] - 29*Log[3] - 54*Log[n] + 123*Log[1 + n] - 72*Log[2 + n] - 10*Log[-1 + 3*n] + 14*Log[1 + 3*n] + 3*n*(Log[729] - 30*Log[n] + Log[1 + n] + 17*Log[2 + n] - 8*Log[-8 + 24*n] + 10*Log[-1 + 9*n^2] + 6*n*(2*n*ArcCoth[3 + 2*n] - 3*Log[n*(1 + n)] + 4*Log[(2 + n)/2] + Log[-3 + 27*n^2])) - 3*Log[((-1 + 9*n^2)*Gamma[4/3]^8)/Pi^4])) + 36*n*(1 + n)*Sum[(1/(2 + k))* ((1/((-(1/3) + n)^k*k) + ((-1 + n)*n^(-1 - k))/ (1 + k) + (-1 + n)/((2 + n)^k*(k*(1 + k))) + ((-1 + 2^k - k)/(2^k*n^k*k) + (1/3 + n)^(-k))/ (1 + k) + (1/(k*(1 + k)*(1 + n)))* ((k*((1/3 + n)*(1 + n))^k*(-1 + n^2) + (2 + n)^k*((1 + n)^(1 + k) + (1/3 + n)^k* (2 + 3*k + n - (1 + k)*n^2)))/ ((1/3 + n)*(1 + n)*(2 + n))^k))*B[2 + k]), {k, 2, Infinity}]) You can even take two terms with n=1: In[674]:= Table[ InputForm[ E^ReleaseHold[%668 /. {n -> 1., \[Infinity] -> k, B -> BernoulliB, z1 -> Zeta'[-1]}]], {k, 1, 23, 2}] Out[674]= {InputForm[1.0103197650836289`], InputForm[ 0.9971632720879865], InputForm[1.0026975018949733`], InputForm[ 0.9945756764366318], InputForm[1.0192129702965944`], InputForm[ 0.9022068215761623], InputForm[2.2230028233909853`], InputForm[ 0.00021460545039988252`], InputForm[ 6.109203829072703*^50], InputForm[ 2.391297463695393665650687064619`12.495500717694712*^-893], \ InputForm[ 1.2327361911718592314255798015869541197472854729273`11.\ 191037729790512*^19431], InputForm[ 1.81378280396368952850445868471`9.881928587042173*^-513388]} and nine with n=3: In[675]:= Table[ InputForm[ E^ReleaseHold[%668 /. {n -> 3., \[Infinity] -> k, B -> BernoulliB, z1 -> Zeta'[-1]}]], {k, 1, 23, 2}] Out[675]= {InputForm[7.0081268915275], InputForm[ 6.999782449734494], InputForm[7.000017783415529], InputForm[ 6.999997135705913], InputForm[7.000000757779692], InputForm[ 6.999999702042258], InputForm[7.000000163276266], InputForm[ 6.999999880868429], InputForm[7.000000111814524], InputForm[ 6.999999868606976], InputForm[7.000000189122515], InputForm[ 6.999999672531021]} And as usual, as many as you like by boosting n via A[n+1]/A[n] = ((n! * (3 * n + 1)!)/((2 * n)! * (2 * n + 1)!)) (which Mathematica can't even *test*, DiscreteRatio having been sandbagged with a mountain of fractional BarnesGs. --rwg Way to go, Adam! Can we start a new found plane thread when they find it?