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Search: id:A095917
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| A095917 |
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Unreduced numerator of Sum[k=1..n, -(-1)^k/(F(k)*F(k+1))], with F(i) = A000045(i) the Fibonacci numbers. |
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+0
1
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| 1, 1, 8, 108, 4500, 460800, 126547200, 90150278400, 168726978201600, 825645617596800000, 10582810279847245440000, 355057327760217947504640000, 31189165230267027857184030720000
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OFFSET
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1,3
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COMMENT
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Denominators are b(n) = Prod[k=1..n, F(k)*F(k+1)] and a(n)/b(n) approaches (sqrt(5)-1)/2.
Can a(n) be expressed in terms of F(n), without the sum? However, the sequence appears not to be C-finite.
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PROGRAM
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(PARI) a(n)=local(f, d, nu):f=sum(k=1, n, -(-1)^k*1/fibonacci(k)/fibonacci(k+1)):d=denominator(f):nu=numerator(f):prod(k=1\ , n, fibonacci(k)*fibonacci(k+1))/d*nu
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CROSSREFS
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Cf. A001654.
Sequence in context: A099699 A084915 A138456 this_sequence A098623 A076151 A020560
Adjacent sequences: A095914 A095915 A095916 this_sequence A095918 A095919 A095920
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 11 2004
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