%I #17 Jun 12 2016 10:11:31
%S 1,1,2,42,2674440,39044429911904443959240,
%T 10934377152170553993439479038404269881062854488806451985760537780703486068308
%N a(n) = Catalan(Catalan(n)).
%C Next term, a(7), which has 255 digits and is equal to Catalan(429), is too large to include.
%C The number of digits of a(n) grows faster than Fibonacci(n) or Catalan(n-1), but slower than Catalan(n).
%F a(n) = A000108(A000108(n)).
%e a(3) = Catalan(Catalan(3)) = Catalan(5) = 42.
%p a:= ((n-> binomial(2*n, n)/(n+1))@@2):
%p seq(a(n), n=0..7); # _Alois P. Heinz_, Jun 12 2016
%t CatalanNumber[CatalanNumber[Range[0,6]]]
%t Table[CatalanNumber[CatalanNumber[n]], {n, 0,6}]
%o for(n=0,6, cn=binomial(2*n, n)/(n+1); cn2=binomial(2*cn, cn)/(cn+1); print1(cn2 ","))
%Y Cf. A000108 (Catalan), A273400 (related sequence).
%K nonn,easy
%O 0,3
%A _Waldemar Puszkarz_, May 21 2016
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