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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

%I #7 Mar 08 2015 13:31:11

%S 1,1,8,108,4500,460800,126547200,90150278400,168726978201600,

%T 825645617596800000,10582810279847245440000,

%U 355057327760217947504640000,31189165230267027857184030720000,7172521863132011354816602281246720000

%N Unreduced numerator of Sum[k=1..n, -(-1)^k/(F(k)*F(k+1))], with F(i) = A000045(i) the Fibonacci numbers.

%C Denominators are b(n) = Prod[k=1..n, F(k)*F(k+1)] and a(n)/b(n) approaches (sqrt(5)-1)/2.

%C Can a(n) be expressed in terms of F(n), without the sum? However, the sequence appears not to be C-finite.

%H Colin Barker, <a href="/A095917/b095917.txt">Table of n, a(n) for n = 1..69</a>

%o (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

%Y Cf. A001654.

%K nonn

%O 1,3

%A _Ralf Stephan_, Jul 11 2004

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)