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

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

Offset

1,3

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000045, A007318, A060001, A001622.

Sequence in context: A192258 A052561 A181927 * A093856 A173097 A088221

Adjacent sequences: A066523 A066524 A066525 * A066527 A066528 A066529

Keyword

easy,nice,nonn

Author

Joe Faust, Jan 05 2002

Extensions

Edited by Robert G. Wilson v, Jan 07 2002

Minor edits by Vaclav Kotesovec, Nov 13 2014

Status

approved