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A066526
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a(n) = binomial(Fibonacci(n), Fibonacci(n-1)).
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5
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1, 1, 2, 3, 10, 56, 1287, 203490, 927983760, 841728816603675, 4404006643598438948468376, 26481463552095445860988385376871250071680, 1057375592689477481644154770179770478007054345083466115864070012050
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OFFSET
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1,3
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LINKS
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FORMULA
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Limit_{n->oo} log(a(n))/log(a(n-1)) = phi follows from Stirling's approximation and the approximation log(F(n)) = n log(phi) + O(1). In fact, log(a(n)) = K phi^n + O(n); the value of K does not matter for this result, but it is log(phi)/phi. - Franklin T. Adams-Watters, Dec 14 2006
a(n) ~ 5^(1/4) * phi^(3/2 - n/2 + phi^(n-1)) / sqrt(2*Pi), where phi = (1+sqrt(5))/2 = A001622. - Vaclav Kotesovec, Nov 13 2014
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EXAMPLE
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a(7) = binomial(Fibonacci(8), Fibonacci(7)) = binomial(21, 13) = 1287.
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MATHEMATICA
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Table[ Binomial[ Fibonacci[n], Fibonacci[n - 1]], {n, 1, 14} ]
Binomial[Last[#], First[#]]&/@Partition[Fibonacci[Range[0, 15]], 2, 1] (* Harvey P. Dale, Oct 15 2014 *)
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PROG
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(PARI) { for (n=1, 18, a=binomial(fibonacci(n), fibonacci(n-1)); write("b066526.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 21 2010
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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