OFFSET
0,2
LINKS
Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27.
FORMULA
Equals Sum_{n>=2} 1/((n-1)^2*binomial(2n,n)).
Sum_{n>=2} (-1)^n/((n-1)^2*binomial(2n,n)) = 1 - sqrt(5)*log(phi) + log(phi)^2 = 0.1555... where phi is the golden ratio.
EXAMPLE
0.181055359925146664709108323262082...
MAPLE
(sqrt(3)+Pi/6)*Pi/6-1; evalf(%) ;
MATHEMATICA
RealDigits[Sqrt[3]*Pi/6 + Pi^2/36 - 1, 10, 120][[1]] (* Amiram Eldar, Jun 10 2024 *)
PROG
(PARI) sqrt(3)*Pi/6 + Pi^2/36 - 1 \\ Amiram Eldar, Jun 10 2024
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Jun 07 2024
STATUS
approved