cp's OEIS Frontend

A261851 Decimal expansion of the central binomial sum S(7), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).

%I A261851 #6 Feb 16 2025 08:33:27
%S A261851 5,0,1,3,2,5,8,7,2,6,8,8,1,7,8,8,0,9,4,0,2,2,9,6,7,1,0,5,5,2,7,4,9,4,
%T A261851 4,3,7,2,6,8,7,8,3,2,9,8,5,8,0,4,5,6,8,1,5,3,6,4,5,1,2,1,7,3,3,8,8,8,
%U A261851 7,4,1,5,8,4,5,0,6,0,6,5,3,3,0,9,0,3,1,1,3,8,8,9,7,9,4,3,9,8,9,6,1,8,1,9,4
%N A261851 Decimal expansion of the central binomial sum S(7), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).
%H A261851 J. M. Borwein, D. J. Broadhurst, J. Kamnitzer, <a href="http://arxiv.org/abs/hep-th/0004153">Central Binomial Sums, Multiple Clausen Values and Zeta Values</a>, arXiv:hep-th/0004153, 2000.
%H A261851 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>
%F A261851 Equals (1/2) 8F7(1,...,1; 3/2,2,...,2; 1/4).
%F A261851 Also equals -6*Pi*Im(-PolyLog(6, (-1)^(1/3))) + (17*Pi^4*zeta(3))/1620 + (1/3)*Pi^2*zeta(5) -  (493*zeta(7))/24.
%e A261851 0.501325872688178809402296710552749443726878329858...
%t A261851 S[7]=-6*Pi*Im[-PolyLog[6, (-1)^(1/3)]] + (17*Pi^4*Zeta[3])/1620 + (1/3)*Pi^2*Zeta[5] - (493*Zeta[7])/24; RealDigits[S[7], 10, 105]//First
%Y A261851 Cf. A073010 (S(1)), A086463 (S(2)), A145438 (S(3)), A086464 (S(4)), A261839 (S(5)), A261850 (S(6)), A261852 (S(8)).
%K A261851 nonn,cons,easy
%O A261851 0,1
%A A261851 _Jean-François Alcover_, Sep 03 2015