A120792 Numerators of partial sums of Catalan numbers scaled by powers of -1/12.

1, 11, 67, 1603, 9625, 4277, 230969, 11086369, 199555357, 2394661853, 14367975317, 344831378215, 2068988321293, 24827859669791, 49655719451017, 1588983021355339, 9533898130096349, 343220332661861099

Offset

0,2

Comments

Denominators are given under A120793.

From the expansion of sqrt(1+1/3) = 1+(1/6)*sum(C(k)/(-12)^k,k=0..infinity) one has, with the partial sums r(n) are defined below, r:=limit(r(n),n to infinity)= 2*(2*sqrt(3)-3)) = 0.9282032302....

Links

Table of n, a(n) for n=0..17.

W. Lang: Rationals r(n) and limit.

Formula

a(n)=numerator(r(n)), with the rationals r(n):=sum(((-1)^k)*C(k)/12^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.

Example

Rationals r(n): [1, 11/12, 67/72, 1603/1728, 9625/10368, 4277/4608,
230969/248832, 11086369/11943936, 199555357/214990848,...].

Crossrefs

Sequence in context: A165673 A220511 A287169 * A228032 A145833 A111931

Adjacent sequences: A120789 A120790 A120791 * A120793 A120794 A120795

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jul 20 2006

Status

approved