A120792 - OEIS

%I #10 Sep 14 2024 06:47:10

%S 1,11,67,1603,9625,4277,230969,11086369,199555357,2394661853,

%T 14367975317,344831378215,2068988321293,24827859669791,49655719451017,

%U 1588983021355339,9533898130096349,343220332661861099

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

%C Denominators are given under A120793.

%C From the expansion of sqrt(1+1/3) = 1+(1/6)*Sum_{k=0..oo} C(k)/(-12)^k one has, with the partial sums r(n) are defined below, r := lim_{n->oo} r(n) = 2*(2*sqrt(3)-3) = 0.9282032302....

%H W. Lang: <a href="/A120792/a120792.txt">Rationals r(n) and limit.</a>

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

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

%K nonn,easy,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 20 2006