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%I #40 Feb 19 2024 10:35:13
%S 1,1,2,3,10,56,1287,203490,927983760,841728816603675,
%T 4404006643598438948468376,26481463552095445860988385376871250071680,
%U 1057375592689477481644154770179770478007054345083466115864070012050
%N a(n) = binomial(Fibonacci(n), Fibonacci(n-1)).
%H Harry J. Smith, <a href="/A066526/b066526.txt">Table of n, a(n) for n = 1..18</a>
%F Limit_{n->oo} log(a(n))/log(a(n-1)) = phi. - _Gerald McGarvey_, Jul 25 2004
%F 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
%F 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
%F a(n) = A060001(n) / (A060001(n-1) * A060001(n-2)). - _Vaclav Kotesovec_, Nov 13 2014
%e a(7) = binomial(Fibonacci(8), Fibonacci(7)) = binomial(21, 13) = 1287.
%t Table[ Binomial[ Fibonacci[n], Fibonacci[n - 1]], {n, 1, 14} ]
%t Binomial[Last[#],First[#]]&/@Partition[Fibonacci[Range[0,15]],2,1] (* _Harvey P. Dale_, Oct 15 2014 *)
%o (PARI) { for (n=1, 18, a=binomial(fibonacci(n), fibonacci(n-1)); write("b066526.txt", n, " ", a) ) } \\ _Harry J. Smith_, Feb 21 2010
%Y Cf. A000045, A007318, A060001, A001622.
%K easy,nice,nonn
%O 1,3
%A _Joe Faust_, Jan 05 2002
%E Edited by _Robert G. Wilson v_, Jan 07 2002
%E Minor edits by _Vaclav Kotesovec_, Nov 13 2014
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