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Search: id:A120792
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| A120792 |
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Numerators of partial sums of Catalan numbers scaled by powers of -1/12. |
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+0
2
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| 1, 11, 67, 1603, 9625, 4277, 230969, 11086369, 199555357, 2394661853, 14367975317, 344831378215, 2068988321293, 24827859669791, 49655719451017, 1588983021355339, 9533898130096349, 343220332661861099
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OFFSET
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0,2
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COMMENT
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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....
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LINKS
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W. Lang: Rationals r(n) and limit.
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FORMULA
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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.
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EXAMPLE
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Rationals r(n): [1, 11/12, 67/72, 1603/1728, 9625/10368, 4277/4608,
230969/248832, 11086369/11943936, 199555357/214990848,...].
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CROSSREFS
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Sequence in context: A035041 A125591 A092841 this_sequence A111931 A066433 A038741
Adjacent sequences: A120789 A120790 A120791 this_sequence A120793 A120794 A120795
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
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