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A095917 Unreduced numerator of Sum[k=1..n, -(-1)^k/(F(k)*F(k+1))], with F(i) = A000045(i) the Fibonacci numbers. 1
1, 1, 8, 108, 4500, 460800, 126547200, 90150278400, 168726978201600, 825645617596800000, 10582810279847245440000, 355057327760217947504640000, 31189165230267027857184030720000, 7172521863132011354816602281246720000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

Colin Barker, Table of n, a(n) for n = 1..69

PROG

(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

CROSSREFS

Cf. A001654.

Sequence in context: A138456 A267660 A273057 * A259233 A322718 A309188

Adjacent sequences:  A095914 A095915 A095916 * A095918 A095919 A095920

KEYWORD

nonn

AUTHOR

Ralf Stephan, Jul 11 2004

STATUS

approved

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Last modified September 22 22:38 EDT 2021. Contains 347609 sequences. (Running on oeis4.)