A066526 a(n) = binomial(Fibonacci(n), Fibonacci(n-1)).

1, 1, 2, 3, 10, 56, 1287, 203490, 927983760, 841728816603675, 4404006643598438948468376, 26481463552095445860988385376871250071680, 1057375592689477481644154770179770478007054345083466115864070012050

Offset: 1

Author

Joe Faust, Jan 05 2002

Keywords

• easy
• nice
• nonn

Examples

			a(7) = binomial(Fibonacci(8), Fibonacci(7)) = binomial(21, 13) = 1287.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..18

Crossrefs

Cf. A000045, A007318, A060001, A001622.

Programs

Mathematica

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 *)

PARI

{ for (n=1, 18, a=binomial(fibonacci(n), fibonacci(n-1)); write("b066526.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 21 2010

Formula

Limit_{n->oo} log(a(n))/log(a(n-1)) = phi. - Gerald McGarvey, Jul 25 2004

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

a(n) = A060001(n) / (A060001(n-1) * A060001(n-2)). - Vaclav Kotesovec, Nov 13 2014

Extensions

Edited by Robert G. Wilson v, Jan 07 2002

Minor edits by Vaclav Kotesovec, Nov 13 2014