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 A120792 Numerators of partial sums of Catalan numbers scaled by powers of -1/12. 2
 1, 11, 67, 1603, 9625, 4277, 230969, 11086369, 199555357, 2394661853, 14367975317, 344831378215, 2068988321293, 24827859669791, 49655719451017, 1588983021355339, 9533898130096349, 343220332661861099 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 23 14:41 EDT 2019. Contains 326249 sequences. (Running on oeis4.)