A060001 -id:A060001 - cp's OEIS frontend

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

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

Offset: 1

Joe Faust, Jan 05 2002

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

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

Cf. A000045, A007318, A060001, A001622.

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 *)

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

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

Edited by Robert G. Wilson v, Jan 07 2002

Minor edits by Vaclav Kotesovec, Nov 13 2014

A261626 a(n) = Fibonacci(n!) - Fibonacci(n)!.

Original entry on oeis.org

0, 0, 0, 6, 46362, 5358359254990966640871720

Offset: 0

Altug Alkan, Sep 14 2015

nonn

			For n = 1, a(n) = Fibonacci(n!) - Fibonacci(n)! = 1 - 1 = 0.

Cf. A000045, A060001, A063374.

a(n) = fibonacci(n!) - fibonacci(n)!;
vector(6, n, a(n-1))

a(n) = A063374(n) - A060001(n).

log log a(n) ~ n log n. - Charles R Greathouse IV, Sep 14 2015

A262776 a(n) = Fibonacci(n!) mod Fibonacci(n)!.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 20160, 1098377280, 10712200669548618240, 157910199555786679826546221836620444160, 12162675222629942931022379230724715707339402614012620710827200735689241600

Offset: 0

Altug Alkan, Oct 01 2015

Inspired by A261626.

Is there a possibility of observing that a(n) = 0 for n > 5?

			a(0) = Fibonacci(0!) mod Fibonacci(0)! = 1 mod 1 = 0.
a(1) = Fibonacci(1!) mod Fibonacci(1)! = 1 mod 1 = 0.
a(2) = Fibonacci(2!) mod Fibonacci(2)! = 1 mod 1 = 0.
a(3) = Fibonacci(3!) mod Fibonacci(3)! = 8 mod 2 = 0.
a(4) = Fibonacci(4!) mod Fibonacci(4)! = 46368 mod 6 = 0.

Alois P. Heinz, Table of n, a(n) for n = 0..14

Cf. A000045, A060001, A063374, A261626.

[Fibonacci(Factorial(n)) mod Factorial(Fibonacci(n)): n in [0..10]]; // Vincenzo Librandi, Oct 01 2015

Table[Mod[Fibonacci[n!], Fibonacci[n]!], {n, 0, 9}] (* Michael De Vlieger, Oct 01 2015 *)

a(n) = fibonacci(n!) % fibonacci(n)!;
vector(10, n, a(n-1))

from gmpy2 import fac, fib
def A262776(n):
    if n < 2:
        return 0
    a, b, m = 0, 1, fac(fib(n))
    for i in range(fac(n)-1):
        b, a = (b+a) % m, b
    return int(b) # Chai Wah Wu, Oct 03 2015

a(n) = A063374(n) mod A060001(n), for n > 0.

a(10) from Alois P. Heinz, Oct 01 2015

A110372 a(n) = F(n+1)!/F(n)! where F(n) = n-th Fibonacci number.

Original entry on oeis.org

1, 2, 3, 20, 336, 154440, 8204716800, 5778574175582208000, 43004718293359780142729736192000000, 1300207208378579462193856077468752280037294977727353323520000000

Offset: 1

Amarnath Murthy, Jul 24 2005

			a(5) = 8!/5! = 336.

Cf. A060001.

with(combinat): seq(fibonacci(n+1)!/fibonacci(n)!,n=1..11); # Emeric Deutsch, Jul 25 2005

More terms from Emeric Deutsch, Jul 25 2005

A262189 a(n) = Fibonacci(n+1)! / Fibonacci(n).

Original entry on oeis.org

1, 2, 3, 40, 8064, 778377600, 3930072474746880000, 14058704716171625754648505221120000000

Offset: 1

Altug Alkan, Sep 14 2015

			For n=2, a(n) = Fibonacci(n+1)! / Fibonacci(n) = 2! / 1 = 2.

Cf. A060001, A000045.

[Factorial(Fibonacci(n+1)) / Fibonacci(n): n in [1..10]]; // Vincenzo Librandi, Sep 15 2015

Array[Fibonacci[# + 1]!/Fibonacci@ # &, {8}] (* Michael De Vlieger, Sep 14 2015 *)

a(n) = fibonacci(n+1)!/fibonacci(n);
vector(10, n, a(n))

a(n) = A060001(n+1) / A000045(n).

cp's OEIS Frontend

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

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A261626 a(n) = Fibonacci(n!) - Fibonacci(n)!.

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A262776 a(n) = Fibonacci(n!) mod Fibonacci(n)!.

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A110372 a(n) = F(n+1)!/F(n)! where F(n) = n-th Fibonacci number.

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A262189 a(n) = Fibonacci(n+1)! / Fibonacci(n).

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