A145564 a(n) = numerator(Sum_{k=0..n} 1/(binomial(2*k,k)*(k+1))).

1, 5, 47, 949, 33287, 14273, 7694047, 400101469, 1200312247, 20405339951, 4264717637359, 328055232193, 1275150714976991, 1275150721602467, 2125251205342781, 246529139894912671, 129920856734238187217, 2122119257040297503, 22216466502052353380347, 164401852115363364287267

Offset

0,2

Comments

Previous name was: "Numerators of partial sums of a certain series of inverse central binomial coefficients.Numerators of partial sums of a certain series of inverse central binomial coefficients".

See A145565 for the denominators.

The limit of the rational partial sums r(n), defined below, for n->infinity is (4*sqrt(3)- Pi)*Pi/9. This limit is approximately 1.321776442.

Links

Table of n, a(n) for n=0..19.

W. 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, fifth identity.

Formula

a(n) = numerator(r(n)) with r(n)=sum(1/(binomial(2*k,k)*(k+1)),k=0..n), rationals in lowest terms.

Example

Rationals r(n) (in lowest terms): [1, 5/4, 47/36, 949/720, 33287/25200, 14273/10800, 7694047/5821200,...].

Prog

(PARI) a(n) = numerator(sum(k=0, n, 1/(binomial(2*k, k)*(k+1)))); \\ Michel Marcus, Nov 08 2015

Crossrefs

Sequence in context: A222078 A061572 A140422 * A159480 A196460 A093612

Adjacent sequences: A145561 A145562 A145563 * A145565 A145566 A145567

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Oct 17 2008

Extensions

New name based on formula by Michel Marcus, Nov 08 2015

Status

approved