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Search: id:A124398
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| A124398 |
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Denominators of partial sums of a series for sqrt(5)/3. |
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2
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| 1, 5, 25, 25, 125, 3125, 15625, 78125, 78125, 390625, 9765625, 48828125, 244140625, 244140625, 48828125, 6103515625, 30517578125, 152587890625, 152587890625, 762939453125, 19073486328125, 95367431640625, 476837158203125
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Denominators of alternating sums over central binomial coefficients scaled by powers of 5.
Numerators are given by A124397.
For the rationals r(n) see the W. Lang link under A124397.
r(n) is not 1/3 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(((-1)^k)*binomial(2*k,k)/5^k,k=0..n) in lowest terms.
r(n)=sum(((-1)^k)*((2*k-1)!!/((2*k)!!)*(4/5)^k,k=0..n),n>=0, with the double factorials A001147 and A000165.
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EXAMPLE
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a(3)=25 because r(3)= 1-2/5+6/25-4/25 = 17/25 = A124397(3)/a(3).
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CROSSREFS
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Adjacent sequences: A124395 A124396 A124397 this_sequence A124399 A124400 A124401
Sequence in context: A036139 A070382 A039936 this_sequence A121003 A121007 A043057
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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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