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A120792 Numerators of partial sums of Catalan numbers scaled by powers of -1/12. 2

%I

%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(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....

%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(((-1)^k)*C(k)/12^k,k=0..n) 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,

%e 230969/248832, 11086369/11943936, 199555357/214990848,...].

%K nonn,easy,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 20 2006

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Last modified September 17 17:32 EDT 2019. Contains 327136 sequences. (Running on oeis4.)