cp's OEIS Frontend

A261850 Decimal expansion of the central binomial sum S(6), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).

%I A261850 #8 Feb 16 2025 08:33:27
%S A261850 5,0,2,6,7,6,5,2,1,4,7,8,2,6,9,2,8,6,4,5,4,6,7,7,4,5,9,9,7,9,3,4,8,6,
%T A261850 3,9,6,6,4,6,0,2,6,0,0,0,9,1,6,4,0,6,6,1,4,6,8,6,2,7,6,5,2,3,2,4,8,7,
%U A261850 1,6,1,5,0,8,8,5,4,6,3,1,2,1,1,7,6,2,3,4,1,5,7,2,7,8,4,0,5,2,7,6,7,8,5,4,1
%N A261850 Decimal expansion of the central binomial sum S(6), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).
%H A261850 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 A261850 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>
%F A261850 Equals (1/2) 7F6(1,1,1,1,1,1,1; 3/2,2,2,2,2,2; 1/4).
%F A261850 Also equals (2/3)*Integral_{0..Pi/3} t*log(2*sin(t/2))^4 dt.
%e A261850 0.50267652147826928645467745997934863966460260009164...
%t A261850 S[6] = Sum[1/(n^6*Binomial[2n, n]), {n, 1, Infinity}]; RealDigits[S[6], 10, 105]//First
%Y A261850 Cf. A073010 (S(1)), A086463 (S(2)), A145438 (S(3)), A086464 (S(4)), A261839 (S(5)), A261851 (S(7)), A261852 (S(8)).
%K A261850 cons,easy,nonn
%O A261850 0,1
%A A261850 _Jean-François Alcover_, Sep 03 2015