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%I #19 Aug 17 2024 23:09:42
%S 1,2,4,12,48,288,2592,36288,798336,27941760,1564738560,140826470400,
%T 20419838208000,4778242140672000,1806175529174016000,
%U 1103573248325323776000,1090330369345419890688000
%N a(n) = Product_{k=1..n} (F(k)+1) where F(k) denotes the k-th Fibonacci number.
%C Equals row sums (unsigned) of triangle A158472. - _Gary W. Adamson_, Mar 20 2009
%F 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
%F 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
%p with(combinat): a:= n->mul(fibonacci(j)+1, j=0..n): seq(a(n), n=0..20); # _Zerinvary Lajos_, Mar 29 2009
%t Table[Product[Fibonacci[k]+1,{k,1,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 19 2015 *)
%o (PARI) a(n)=prod(k=1,n,fibonacci(k)+1)
%Y Cf. A000045, A158472. - _Gary W. Adamson_, Mar 20 2009
%K nonn
%O 0,2
%A _Benoit Cloitre_, Apr 27 2003