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Search: id:A124396
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| A124396 |
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Denominators of partial sums of a series for 3/sqrt(5) = (3/5)*sqrt(5). |
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3
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| 1, 9, 27, 729, 6561, 6561, 177147, 1594323, 4782969, 387420489, 3486784401, 10460353203, 282429536481, 2541865828329, 2541865828329, 22876792454961, 205891132094649, 617673396283947, 50031545098999707, 450283905890997363
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OFFSET
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0,2
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COMMENT
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Denominators of sums over central binomial coefficients scaled by powers of 9.
Numerators are given by A123749.
For the rationals r(n) see the W. Lang link under A123749.
This is not 3/5 times the rational sequence A123747/A123748 which converges to sqrt(5).
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FORMULA
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a(n)=denominator(r(n)) with the rationals r(n):=sum(binomial(2*k,k)/9^k,k=0..n) in lowest terms.
r(n)=sum(((2*k-1)!!/((2*k)!!)*(4/9)^k,k=0..n),n>=0, with the double factorials A001147 and A000165.
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EXAMPLE
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a(3)=729 because r(3)=1+2/9+2/27+20/729 = 965/729 = A123749(3)/a(3).
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CROSSREFS
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Cf. A123747/A123748 partial sums for a series for sqrt(5).
Sequence in context: A020279 A057901 A020254 this_sequence A020281 A075539 A053825
Adjacent sequences: A124393 A124394 A124395 this_sequence A124397 A124398 A124399
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 10 2006
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