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A273398 a(n) = Catalan(Fibonacci(n)).

%I A273398 #15 Jan 20 2017 18:27:58
%S A273398 1,1,1,2,5,42,1430,742900,24466267020,812944042149730764,
%T A273398 1759414616608818870992479875972,
%U A273398 254224158304000796523953440778841647086547372026600,161115593562260183597018076262500259385225118963936327496691227156776984827584194180
%N A273398 a(n) = Catalan(Fibonacci(n)).
%C A273398 Next term, a(13), which has 137 digits, is too large to include. Counterpart to A273397.
%C A273398 The number of digits of a(n) grows fast exceeding 10^6 for n=32. It grows faster than Fibonacci(n-2) but slower than Fibonacci(n) or Fibonacci(n-1) and even slower than the same number for A273397 which grows faster than Fibonacci(n).
%H A273398 Alois P. Heinz, <a href="/A273398/b273398.txt">Table of n, a(n) for n = 0..17</a>
%F A273398 a(n) = A000108(A000045(n)).
%e A273398 For n=4, a(4)=Catalan(Fibonacci(4))=Catalan(3)=5.
%p A273398 a:= n-> (f-> binomial(2*f, f)/(f+1))((<<0|1>, <1|1>>^n)[1, 2]):
%p A273398 seq(a(n), n=0..12);  # _Alois P. Heinz_, Jan 20 2017
%t A273398 CatalanNumber[Fibonacci[Range[0,12]]]
%t A273398 Table[CatalanNumber[Fibonacci[n]], {n, 0,12}]
%o A273398 (PARI) for(n=0,12, fn=fibonacci(n); print1(binomial(2*fn, fn)/(fn+1) ","))
%Y A273398 Cf. A000108(Catalan), A000045 (Fibonacci), A263986, A273397 (related sequences with Fibonacci and Catalan numbers).
%K A273398 nonn,easy
%O A273398 0,4
%A A273398 _Waldemar Puszkarz_, May 21 2016