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a(n) = Fibonacci(n!).
5

%I #16 Dec 07 2019 12:18:22

%S 1,1,1,8,46368,5358359254990966640871840,

%T 1323171012053243520828784042795469593341319770463238313551473338336502410952765153371119398122747569819754164672344667591018783803781288766524146031040

%N a(n) = Fibonacci(n!).

%p a:= n-> (<<0|1>, <1|1>>^(n!))[1, 2]:

%p seq(a(n), n=0..6); # _Alois P. Heinz_, Jun 10 2018

%t Array[Fibonacci[ #! ]&,7] (* _Vladimir Joseph Stephan Orlovsky_, Nov 01 2009 *)

%o (PARI) for(n=0,6,print(fibonacci(n!)))

%o (Sage) [fibonacci(factorial(n)) for n in range(0, 9)] # _Zerinvary Lajos_, Nov 30 2009

%Y Cf. A000045.

%K nonn

%O 0,4

%A _Jason Earls_, Jul 23 2001