OFFSET
1,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
Thotsaporn Aek Thanatipanonda and Yi Zhang, Sequences: Polynomial, C-finite, Holonomic, ..., arXiv:2004.01370 [math.CO], 2020.
FORMULA
For n >= 2, a(n) = (F(n-1) + 1)*a(n-1); a(n) = (1/2)*Product_{k=1..n-1} (F(k)+1).
G.f.: 1 + x/(G(0)-2*x) where G(k) = 1 + x + x*F(k+1) - x*(F(k+2)+1)/G(k+1); F(k) is the k-th Fibonacci number; (continued fraction). - Sergei N. Gladkovskii, Jul 08 2012
a(n) ~ c * ((1+sqrt(5))/2)^(n*(n-1)/2) / 5^(n/2), where c = 18.0370671229828603013612398720270653807943654417062957419698762672485... - Vaclav Kotesovec, Aug 14 2017
MATHEMATICA
Join[{1}, 1/2 Table[Product[Fibonacci[k] + 1, {k, 1, n}], {n, 1, 20}]] (* Vincenzo Librandi, Aug 14 2017 *)
PROG
(PARI) a(n) = if (n==1, 1, prod(k=1, n-1, fibonacci(k)+1)/2); \\ Michel Marcus, Aug 14 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 27 2003
EXTENSIONS
More terms from Michel Marcus, Aug 14 2017
STATUS
approved