This constant is mentioned in GKP book : 

Concrete Mathematics, by Ron Graham, Donald E Knuth, Oren Patashnik
page 478 and 571. Addison Wesley, 1990.

1.2267420107203532444176302304553616558714096904402504196432973012140221383153\
121684526215624947977412591332334004120027440664103145209506733881793040788634\
483048008841808185478343494023885863335310549643887562213037246127723118581180\
56699615948964051109218

   is 256 digits of that constant C.


The Fibonacci factorials, FF(n) are the

  Product(Fibonacci(k),k=1..n) 

so FF(5) = 1*1*2*3*5 = 30 and FF(100) = roughly 10 ** 1021.

Since F(n) is {phi**n/sqrt(5)} , rounded to the 
nearest integer , then we can easily say that
     
       FF(n) will be roughly phi**(n*(n+1)/2)/sqrt(5)**n    (1)

  where phi is the Golden ratio = 1/2 + sqrt(5)/2,

so by examining the sum of the log of F(n) (the fibonacci sequence)

we can expand it to find more precisely that the expression (1)
will involve a constant C, namely FF(n) = C * phi**(n*(n+1)/2)/sqrt(5)**n

 and that C = (1-a)*(1-a**2)*(1-a**3)... 1.2267420...
 where a = -1/phi**2.

This product (with a) is the inverse of the partition function where the 
exponents are pentoganal numbers, maybe there is a closed expression for C ??

For further details see GKP book page 571.


































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