login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194158 Product of first n nonzero odd-indexed Fibonacci numbers F(1), ..., F(2*n-1). 7
1, 2, 10, 130, 4420, 393380, 91657540, 55911099400, 89290025741800, 373321597626465800, 4086378207619294646800, 117103340295746126693347600, 8785678105688353155168403690000, 1725665322163094950031867515982420000, 887387152950606153059937200876123854180000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The terms of this sequence are Fibonacci double factorial numbers.

The a(n) is asymptotic to C1*phi^(n*n)/sqrt(5)^n where phi=(1+sqrt(5))/2 is the golden ratio A001622. For the decimal expansion of C1 see A194160.

REFERENCES

Ronald L. Graham, Donald E. Knuth and Oren Patashnik, Concrete Mathematics, 6th printing with corrections. Addison-Wesley, Reading, MA, p. 478 and p. 571, 1990.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..69

Eric Weisstein's World of Mathematics, Fibonorial

FORMULA

a(n) = Product_{i=1..n} F(2*i-1), where F(n) = A000045(n).

a(n) = A123029(2*n-1).

a(n+1)/a(n) = A001519(n+1).

a(0) = 1 by convention since empty products equal 1. - Michael Somos, Oct 07 2014

a(-n) = 1/a(n) for all n in Z. - Michael Somos, Oct 07 2014

0 = a(n)*(+a(n+1)*a(n+3) - 3*a(n+2)^2) + a(n+2)*(+a(n+1)^2) for all n in Z. - Michael Somos, Oct 07 2014

EXAMPLE

G.f. = 1 + x + 2*x^2 + 10*x^3 + 130*x^4 + 4420*x^5 + 393380*x^6 + 91657540*x^7 + ...

MAPLE

with(combinat): A194158 :=proc(n): mul(fibonacci(2*i-1), i=1..n) end: seq(A194158(n), n=1..15);

MATHEMATICA

Table[Product[Fibonacci[2*k - 1], {k, 1, n}], {n, 1, 30}] (* G. C. Greubel, Aug 13 2018 *)

PROG

(PARI) {a(n) = if( n<0, 1 / a(-n), prod(k=1, n, fibonacci(2*k - 1)))}; /* Michael Somos, Oct 07 2014 */

CROSSREFS

Cf. A003266, A062073, A194158, A194160, A194157, A194159, A123029.

Sequence in context: A258971 A011805 A294350 * A323715 A111135 A097928

Adjacent sequences:  A194155 A194156 A194157 * A194159 A194160 A194161

KEYWORD

nonn,easy

AUTHOR

Johannes W. Meijer, Aug 21 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)