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A066526 a(n) = binomial(Fibonacci(n), Fibonacci(n-1)). 4
1, 1, 2, 3, 10, 56, 1287, 203490, 927983760, 841728816603675, 4404006643598438948468376, 26481463552095445860988385376871250071680, 1057375592689477481644154770179770478007054345083466115864070012050 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

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

Lim_{n->infinity} 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.

MAPLE

with(combinat): P:=proc(q) local n; for n from 1 to q do

print(binomial(fibonacci(n), fibonacci(n-1)));

od; end: P(20); # Paolo P. Lava, Feb 04 2015

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

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Last modified April 9 04:05 EDT 2020. Contains 333343 sequences. (Running on oeis4.)