OFFSET
1,2
LINKS
Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27.
FORMULA
Equals Sum_{n>=0} 1/((n+1)*binomial(2n,n)).
The alternating case is Sum_{n>=0} (-1)^n/((n+1)*binomial(2*n,n)) = 8*log(phi)/sqrt(5)-4*log^2(phi) = 0.79537... where phi is the golden ratio.
EXAMPLE
1.321776441080139509810494232425524183566...
MAPLE
4*Pi/3^(3/2)-Pi^2/9 ; evalf(%) ;
MATHEMATICA
RealDigits[4*Pi/3^(3/2) - Pi^2/9, 10, 120][[1]] (* Amiram Eldar, Jun 10 2024 *)
PROG
(PARI) 4*Pi/3^(3/2) - Pi^2/9 \\ Amiram Eldar, Jun 10 2024
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Jun 07 2024
STATUS
approved