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A273398
a(n) = Catalan(Fibonacci(n)).
2
1, 1, 1, 2, 5, 42, 1430, 742900, 24466267020, 812944042149730764, 1759414616608818870992479875972, 254224158304000796523953440778841647086547372026600, 161115593562260183597018076262500259385225118963936327496691227156776984827584194180
OFFSET
0,4
COMMENTS
Next term, a(13), which has 137 digits, is too large to include. Counterpart to A273397.
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).
LINKS
FORMULA
a(n) = A000108(A000045(n)).
EXAMPLE
For n=4, a(4)=Catalan(Fibonacci(4))=Catalan(3)=5.
MAPLE
a:= n-> (f-> binomial(2*f, f)/(f+1))((<<0|1>, <1|1>>^n)[1, 2]):
seq(a(n), n=0..12); # Alois P. Heinz, Jan 20 2017
MATHEMATICA
CatalanNumber[Fibonacci[Range[0, 12]]]
Table[CatalanNumber[Fibonacci[n]], {n, 0, 12}]
PROG
(PARI) for(n=0, 12, fn=fibonacci(n); print1(binomial(2*fn, fn)/(fn+1) ", "))
CROSSREFS
Cf. A000108(Catalan), A000045 (Fibonacci), A263986, A273397 (related sequences with Fibonacci and Catalan numbers).
Sequence in context: A075891 A246669 A208302 * A116297 A215170 A286871
KEYWORD
nonn,easy
AUTHOR
Waldemar Puszkarz, May 21 2016
STATUS
approved