cp's OEIS Frontend

A261852 Decimal expansion of the central binomial sum S(8), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).

%I A261852 #6 Feb 16 2025 08:33:27
%S A261852 5,0,0,6,5,8,8,9,1,2,9,7,6,7,0,5,4,3,3,1,4,5,5,7,1,2,7,0,8,2,9,8,6,8,
%T A261852 3,8,3,8,4,0,7,3,2,5,2,3,4,0,4,5,4,0,3,8,8,8,8,6,4,3,8,0,4,7,6,6,2,1,
%U A261852 7,1,8,2,0,3,3,4,1,3,5,8,7,6,5,4,5,6,6,2,7,0,9,0,8,1,5,1,6,7,7,2
%N A261852 Decimal expansion of the central binomial sum S(8), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).
%H A261852 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 A261852 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>
%F A261852 Equals (1/2) 8F7(1,...,1; 3/2,2,...,2; 1/4).
%F A261852 Also equals (4/45)*Integral_{0..Pi/3} t*log(2*sin(t/2))^6 dt.
%e A261852 0.5006588912976705433145571270829868383840732523404540388886438...
%t A261852 S[8] = Sum[1/(n^8*Binomial[2n, n]), {n, 1, Infinity}]; RealDigits[S[8], 10, 100] // First
%Y A261852 Cf. A073010 (S(1)), A086463 (S(2)), A145438 (S(3)), A086464 (S(4)), A261839 (S(5)), A261850 (S(6)), A261851 (S(7)).
%K A261852 nonn,cons,easy
%O A261852 0,1
%A A261852 _Jean-François Alcover_, Sep 03 2015