OFFSET
1,2
COMMENTS
Denominators are given in A130554.
The rational sequence r(n) = 2*Sum_{j=1..n} 1/(j*binomial(2*j,j)), n >= 1, tends, in the limit as n->infinity, to 2*Pi*sqrt(3)/9, which is approximately 1.209199577.
With offset 0 the rationals r(n) coincide with Sum_{j=0..n} 1/((2*j+1)*binomial(2*j,j)), n >= 0. See e.g. the Sprugnoli reference. [Wolfdieter Lang, Oct 17 2008]
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Exercise.
LINKS
C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45. 2*Eq. 10, p. 38. [Wolfdieter Lang, Oct 17 2008]
W. Lang, Rationals and limit.
Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, Integers: electronic journal of combinatorial number theory, 6 (2006) #A27, 1-18. [Wolfdieter Lang, Oct 17 2008]
FORMULA
a(n) = numerator(r(n)), n >= 1, with the rationals r(n) defined above and taken in lowest terms.
EXAMPLE
Rationals r(n): 1, 7/6, 6/5, 169/140, 1523/1260, 133/110, 72623/60060, ....
PROG
(PARI) a(n) = numerator(2*sum(j=1, n, 1/(j*binomial(2*j, j)))); \\ Michel Marcus, Nov 08 2015
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Jul 13 2007
STATUS
approved