A145566 a(n) = numerator(6 * Sum_{k=2..n} 1/(binomial(2*k, k)*(k-1))).

1, 23, 33, 199, 10957, 11873, 35621, 4844519, 2789277, 2789279, 705687707, 1764219339, 3175594841, 26312071601, 79968060793, 479808364823, 57097195415809, 234732914489081, 704198743468603, 28872148482226289, 17992788184577863, 161935093661205289

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

Table of n, a(n) for n=2..23.

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

Sequence in context: A038356 A043129 A043909 * A146595 A230123 A049851

Adjacent sequences: A145563 A145564 A145565 * A145567 A145568 A145569

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