A082471 a(1)=1, a(n) = Sum_{k=1..n-1} Fibonacci(k)*a(k).

1, 1, 2, 6, 24, 144, 1296, 18144, 399168, 13970880, 782369280, 70413235200, 10209919104000, 2389121070336000, 903087764587008000, 551786624162661888000, 545165184672709945344000, 871173965106990492659712000, 2251984699801570423525355520000

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

Cf. A003266.

Sequence in context: A375808 A258325 A191006 * A275594 A013010 A275955

Adjacent sequences: A082468 A082469 A082470 * A082472 A082473 A082474

Keyword

nonn

Author

Benoit Cloitre, Apr 27 2003

Extensions

More terms from Michel Marcus, Aug 14 2017

Status

approved