OFFSET
0,1
COMMENTS
This is to A000032 as A003266 is to A000045. a(n) is asymptotic to C*phi^(n*(n+1)/2) where phi=(1+sqrt(5))/2 is the golden ratio and C = 1.3578784076121057013874397... (see A218490). - Corrected and extended by Vaclav Kotesovec, Oct 30 2012
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..95
FORMULA
a(n) = Product_{k=0..n} A000032(k).
C = exp( Sum_{k>=1} 1/(k*(((3-sqrt(5))/2)^k-(-1)^k)) ). - Vaclav Kotesovec, Jun 08 2013
From Amiram Eldar, Dec 27 2025: (Start)
a(n) = 2*A070825(n).
Sum_{n>=0} 1/a(n) = (1 + A101690)/2. (End)
EXAMPLE
a(0) = L(0) = 2.
a(1) = L(0)*L(1) = 2*1 = 2.
a(2) = L(0)*L(1)*L(2) = 2*1*3 = 6.
a(3) = L(0)*L(1)*L(2)*L(3) = 2*1*3*4 = 24.
MATHEMATICA
Rest[FoldList[Times, 1, LucasL[Range[0, 20]]]] (* Harvey P. Dale, Aug 21 2013 *)
Table[Round[GoldenRatio^(n(n+1)/2) QPochhammer[-1, GoldenRatio-2, n+1]], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 14 2016 *)
PROG
(PARI) a(n) = prod(k=0, n, fibonacci(k+1)+fibonacci(k-1)); \\ Michel Marcus, Oct 13 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Dec 09 2007
STATUS
approved
