A082480 a(n) = Product_{k=1..n} (F(k)+1) where F(k) denotes the k-th Fibonacci number.

1, 2, 4, 12, 48, 288, 2592, 36288, 798336, 27941760, 1564738560, 140826470400, 20419838208000, 4778242140672000, 1806175529174016000, 1103573248325323776000, 1090330369345419890688000

Offset

0,2

Comments

Equals row sums (unsigned) of triangle A158472. - Gary W. Adamson, Mar 20 2009

Links

Table of n, a(n) for n=0..16.

Formula

a(n) ~ f * C * ((1+sqrt(5))/2)^(n*(n+1)/2) / 5^(n/2), where C = A062073 = 1.2267420107203532444176302304553616558714096904402504196432973... is the Fibonacci factorial constant and f = Product_{k>=1} (1 + 1/Fibonacci(k)) = 13.150966657784184367612433370626658932190199543164284701354100747157698046... . - Vaclav Kotesovec, Jul 19 2015

Equals the obverse convolution of A000012 and A000045; see A374848. a(n) = (F(n)+1)*a(n-1) for n>=1, where F(n) = A000045(n) = n-th Fibonacci number. - Clark Kimberling, Aug 05 2024

Maple

with(combinat): a:= n->mul(fibonacci(j)+1, j=0..n): seq(a(n), n=0..20); # Zerinvary Lajos, Mar 29 2009

Mathematica

Table[Product[Fibonacci[k]+1, {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 19 2015 *)

Prog

(PARI) a(n)=prod(k=1, n, fibonacci(k)+1)

Crossrefs

Cf. A000045, A158472. - Gary W. Adamson, Mar 20 2009

Sequence in context: A263867 A326863 A372145 * A093934 A109458 A375516

Adjacent sequences: A082477 A082478 A082479 * A082481 A082482 A082483

Keyword

nonn

Author

Benoit Cloitre, Apr 27 2003

Status

approved