OFFSET
2,2
COMMENTS
Previous name was: "Numerators of partial sums of a certain series of inverse central binomial coefficients".
See A145567 for the denominators/6.
The limit of the rational partial sums r(n), defined below, for n->infinity is (9 - sqrt(3)*Pi)/3. This limit is approximately 1.186200635.
LINKS
Wolfdieter Lang, Rationals and more.
Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, Integers: electronic journal of combinatorial number theory, 6 (2006) #A27, 1-18. Theorem 3.4, sixth identity times 6.
EXAMPLE
Rationals 6*r(n) (in lowest terms): [1, 23/20, 33/28, 199/168, 10957/9240, 11873/10010, 35621/30030, 4844519/4084080,...].
MAPLE
a := n -> numer(6*add(1/(binomial(2*k, k)*(k-1)), k=2..n)):
seq(a(n), n = 2..23); # Peter Luschny, Jun 12 2022
PROG
(PARI) a(n) = numerator(6*sum(k=2, n, 1/(binomial(2*k, k)*(k-1)))); \\ Michel Marcus, Nov 08 2015; with factor 6 by Georg Fischer, Jun 11 2022
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Oct 17 2008
EXTENSIONS
New name based on formula by Michel Marcus, Nov 08 2015
Definition amended by Georg Fischer, Jun 12 2022
STATUS
approved