OFFSET
0,1
LINKS
J. M. Borwein, D. J. Broadhurst, J. Kamnitzer, Central Binomial Sums, Multiple Clausen Values and Zeta Values, arXiv:hep-th/0004153, 2000.
Eric Weisstein's MathWorld, Central Binomial Coefficient
FORMULA
Equals (1/2) 7F6(1,1,1,1,1,1,1; 3/2,2,2,2,2,2; 1/4).
Also equals (2/3)*Integral_{0..Pi/3} t*log(2*sin(t/2))^4 dt.
EXAMPLE
0.50267652147826928645467745997934863966460260009164...
MATHEMATICA
S[6] = Sum[1/(n^6*Binomial[2n, n]), {n, 1, Infinity}]; RealDigits[S[6], 10, 105]//First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Sep 03 2015
STATUS
approved