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A273399
a(n) = Catalan(Catalan(n)).
1
1, 1, 2, 42, 2674440, 39044429911904443959240, 10934377152170553993439479038404269881062854488806451985760537780703486068308
OFFSET
0,3
COMMENTS
Next term, a(7), which has 255 digits and is equal to Catalan(429), is too large to include.
The number of digits of a(n) grows faster than Fibonacci(n) or Catalan(n-1), but slower than Catalan(n).
FORMULA
a(n) = A000108(A000108(n)).
EXAMPLE
a(3) = Catalan(Catalan(3)) = Catalan(5) = 42.
MAPLE
a:= ((n-> binomial(2*n, n)/(n+1))@@2):
seq(a(n), n=0..7); # Alois P. Heinz, Jun 12 2016
MATHEMATICA
CatalanNumber[CatalanNumber[Range[0, 6]]]
Table[CatalanNumber[CatalanNumber[n]], {n, 0, 6}]
PROG
for(n=0, 6, cn=binomial(2*n, n)/(n+1); cn2=binomial(2*cn, cn)/(cn+1); print1(cn2 ", "))
CROSSREFS
Cf. A000108 (Catalan), A273400 (related sequence).
Sequence in context: A330229 A039622 A130506 * A052078 A069544 A256285
KEYWORD
nonn,easy
AUTHOR
Waldemar Puszkarz, May 21 2016
STATUS
approved