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

1, 1, 1, 2, 5, 42, 1430, 742900, 24466267020, 812944042149730764, 1759414616608818870992479875972, 254224158304000796523953440778841647086547372026600, 161115593562260183597018076262500259385225118963936327496691227156776984827584194180

Offset: 0

Author

Waldemar Puszkarz, May 21 2016

Keywords

• nonn
• easy

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).

Examples

			For n=4, a(4)=Catalan(Fibonacci(4))=Catalan(3)=5.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..17

Crossrefs

Cf. A000108(Catalan), A000045 (Fibonacci), A263986, A273397 (related sequences with Fibonacci and Catalan numbers).

Programs

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}]

PARI

for(n=0,12, fn=fibonacci(n); print1(binomial(2*fn, fn)/(fn+1) ","))

Formula

a(n) = A000108(A000045(n)).