OFFSET
0,3
LINKS
C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.
FORMULA
Sum_{i >= 1} 1/(i*C(2*i, i)) = Pi*sqrt(3)/9.
EXAMPLE
0, 1/2, 7/12, 3/5, 169/280, 1523/2520, 133/220, 72623/120120, 87149/144144, .... -> Pi*sqrt(3)/9.
MATHEMATICA
Join[{0}, Accumulate[Table[1/(x Binomial[2x, x]), {x, 30}]]]//Numerator (* Harvey P. Dale, May 08 2022 *)
PROG
(PARI) a(n) = numerator(sum(i=1, n, 1/(i*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 30 2005
EXTENSIONS
Definition corrected by Wolfdieter Lang, Oct 07 2008
STATUS
approved