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Search: id:A120788
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| A120788 |
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Numerators of partial sums of Catalan numbers scaled by powers of -1/4. |
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+0
3
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| 1, 3, 7, 51, 109, 415, 863, 13379, 27473, 107461, 219121, 1723575, 3499153, 13810887, 27956079, 884899683, 1787478201, 7085090409, 14289590493, 113433092349, 228507214803, 907912292457, 1827259905369
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Denominators are given under A120777.
From the expansion of sqrt(2) = 1+(1/2)*sum(C(k)/(-4)^k,k=0..infinity) one has, with the partial sums r(n) are defined below, r:=limit(r(n),n to infinity)= 2*(sqrt(2)-1) = 0.828427124....
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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)/4^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, 3/4, 7/8, 51/64, 109/128, 415/512, 863/1024,
13379/16384, 27473/32768, 107461/131072, 219121/262144,...].
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CROSSREFS
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Sequence in context: A113775 A113236 A035499 this_sequence A041277 A095124 A144030
Adjacent sequences: A120785 A120786 A120787 this_sequence A120789 A120790 A120791
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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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