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%I #26 Sep 08 2022 08:45:52
%S 0,1,2,5,16,81,649,8438,177199,6024767,331362186,29491234555,
%T 4246737775921,989489901789594,373037692974676939,
%U 227552992714552932791,224594803809263744664718,358677901683394200229554647,926823697949890613393169207849
%N a(n) = Fibonacci(n)*a(n-1) + 1, a(0) = 0.
%H Vincenzo Librandi, <a href="/A176343/b176343.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = Fibonacci(n)*a(n-1) + 1, a(0) = 0.
%F a(n) ~ c * ((1+sqrt(5))/2)^(n^2/2+n/2) / 5^(n/2), where c = A062073 * A101689 = 3.317727324507285486862890025085971028467... is product of Fibonacci factorial constant (see A062073) and Sum_{n>=1} 1/(Product_{k=1..n} A000045(k) ). - _Vaclav Kotesovec_, Feb 20 2014
%p with(combinat);
%p a:= proc(n) option remember;
%p if n=0 then 0
%p else 1 + fibonacci(n)*a(n-1)
%p fi; end:
%p seq( a(n), n=0..20); # _G. C. Greubel_, Dec 07 2019
%t a[n_]:= a[n]= If[n==0, 0, Fibonacci[n]*a[n-1] +1]; Table[a[n], {n,0,20}]
%o (PARI) a(n) = if(n==0, 0, 1 + fibonacci(n)*a(n-1) ); \\ _G. C. Greubel_, Dec 07 2019
%o (Magma)
%o function a(n)
%o if n eq 0 then return 0;
%o else return 1 + Fibonacci(n)*a(n-1);
%o end if; return a; end function;
%o [a(n): n in [0..20]]; // _G. C. Greubel_, Dec 07 2019
%o (Sage)
%o def a(n):
%o if (n==0): return 0
%o else: return 1 + fibonacci(n)*a(n-1)
%o [a(n) for n in (0..20)] # _G. C. Greubel_, Dec 07 2019
%o (GAP)
%o a:= function(n)
%o if n=0 then return 0;
%o else return 1 + Fibonacci(n)*a(n-1);
%o fi; end;
%o List([0..20], n-> a(n) ); # _G. C. Greubel_, Dec 07 2019
%Y Cf. A000045, A003266, A062073, A101689, A139339, A238243, A238244.
%K nonn,easy
%O 0,3
%A _Roger L. Bagula_, Apr 15 2010
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