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/C(2*i, i) = (2*Pi*sqrt(3) + 9)/27.
EXAMPLE
0, 1/2, 2/3, 43/60, 307/420, 463/630, 10201/13860, 24121/32760, 88453/120120, ... -> (2*Pi*sqrt(3) + 9)/27.
MAPLE
BB:=n->sum(1/binomial(2*i, i), i=1..n): a:=n->floor(numer(BB(n))): seq(a(n), n=0..23); # Zerinvary Lajos, Mar 28 2007
MATHEMATICA
Numerator@ Table[Sum[1/Binomial[2 i, i], {i, n}], {n, 0, 23}] (* Michael De Vlieger, Mar 09 2016 *)
PROG
(PARI) a(n) = numerator(sum(i=1, n, 1/binomial(2*i, i))); \\ Michel Marcus, Mar 09 2016
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 30 2005
STATUS
approved