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%I #21 Jan 21 2017 19:01:45
%S 1,1,1,5,377,267914296,1725375039079340637797070384,
%T 202401005213503038261932567177107618332887918916819829782797456368284639448671475316218754
%N a(n) = Fibonacci(Catalan(n)).
%C Next term, a(8), which has 299 digits, is too large to include. Counterpart to A273398.
%C The number of digits of a(n) grows faster than Fibonacci(n), in contrast to A273398, and faster than Catalan(n-2), but slower than Catalan(n-1) or Catalan(n).
%H Alois P. Heinz, <a href="/A273397/b273397.txt">Table of n, a(n) for n = 0..8</a>
%F a(n) = A000045(A000108(n)).
%e For n = 3, a(3) = Fibonacci(Catalan(3)) = Fibonacci(5) = 5.
%p a:= n-> (<<0|1>, <1|1>>^(binomial(2*n, n)/(n+1)))[1, 2]:
%p seq(a(n), n=0..8); # _Alois P. Heinz_, Jan 20 2017
%t Fibonacci[CatalanNumber[Range[0, 7]]]
%o (PARI) for(n=0,7, cn=binomial(2*n, n)/(n+1); print1(fibonacci(cn) ","))
%Y Cf. A000045 (Fibonacci), A000108(Catalan), A263986, A273398 (related sequences with Fibonacci and Catalan numbers), A281450.
%K nonn,easy
%O 0,4
%A _Waldemar Puszkarz_, May 21 2016
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