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Search: id:A123748
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| A123748 |
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Denominators of partial sums of a series for sqrt(5). |
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+0
6
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| 1, 5, 25, 5, 125, 3125, 15625, 78125, 78125, 390625, 9765625, 48828125, 244140625, 244140625, 78125, 6103515625, 30517578125, 152587890625, 152587890625, 762939453125, 19073486328125, 95367431640625, 476837158203125
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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 5.
Numerators are given by A123747.
For the rationals r(n) see the W. Lang link under A123747.
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FORMULA
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a(n)=denominator(r(n)) with the rationals r(n):=sum(binomial(2*k,k)/5^k,k=0..n) in lowest terms.
r(n)=sum(((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)=5 because r(3)= 1+2/5+6/25+4/25 = 9/5 = A123747(3)/a(3).
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CROSSREFS
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Sequence in context: A051812 A003224 A070387 this_sequence A050108 A070386 A050084
Adjacent sequences: A123745 A123746 A123747 this_sequence A123749 A123750 A123751
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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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