A152686 Partial products of the partial products of the nonzero Fibonacci numbers.

1, 1, 1, 2, 12, 360, 86400, 269568000, 17662095360000, 39345496591564800000, 4820704671590339051520000000, 52567343238846954009129910272000000000, 82543717140049422917575408530662149324800000000000

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 10 2008

Keywords

• nonn

Comments

Partial products of A003266.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..31

Crossrefs

Cf. A001924, A003266, A062381, A253267.

Programs

Mathematica

Table[Product[Product[Fibonacci[k],{k,1,j}],{j,1,n}],{n,1,12}] (* Vaclav Kotesovec, May 01 2015 *)

Formula

a(n) = Product_{i=1..n} A003266(i). - R. J. Mathar, Dec 12 2008

a(n) ~ f * ((1+sqrt(5))/2)^(n*(n+1)*(n+2)/6) * C^n / 5^(n*(n+1)/4), where C = A062073 = 1.2267420107203532444176302... is the Fibonacci factorial constant and f = A253267 = 1.096414072507324423110215998844440375945929608777697938465... . - Vaclav Kotesovec, May 01 2015

Extensions

Edited by R. J. Mathar, Dec 12 2008

a(0)=1 prepended by Alois P. Heinz, Sep 14 2018