OFFSET
1,2
COMMENTS
Partial sums (in lowest terms) for a series of (2/27)*(9+2*Pi*sqrt(3)).
The rationals r(n) = 2*Sum_{k=1..n} 1/binomial(2*k,k) tend, in the limit n->infinity, to (2/27)*(9 + 2*Pi*sqrt(3)), which is approximately 1.472799718.
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Exercise (with a misprint).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
W. Lang, Rationals and limit.
FORMULA
a(n) = numerator(r(n)), n >= 1, with the rationals defined above.
EXAMPLE
Rationals r(n): 1, 4/3, 43/30, 307/210, 463/315, 10201/6930, 24121/16380, ....
MATHEMATICA
Numerator[Table[2*Sum[1/Binomial[2k, k], {k, n}], {n, 30}]] (* Harvey P. Dale, Jul 30 2015 *)
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Jul 13 2007
STATUS
approved