A263986 -id:A263986 - cp's OEIS frontend

A273397 a(n) = Fibonacci(Catalan(n)).

1, 1, 1, 5, 377, 267914296, 1725375039079340637797070384, 202401005213503038261932567177107618332887918916819829782797456368284639448671475316218754

Offset: 0

Waldemar Puszkarz, May 21 2016

Next term, a(8), which has 299 digits, is too large to include. Counterpart to A273398.

The number of digits of a(n) grows faster than Fibonacci(n), in contrast to A273398, and faster than Catalan(n-2), but slower than Catalan(n-1) or Catalan(n).

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

Alois P. Heinz, Table of n, a(n) for n = 0..8

Cf. A000045 (Fibonacci), A000108(Catalan), A263986, A273398 (related sequences with Fibonacci and Catalan numbers), A281450.

a:= n-> (<<0|1>, <1|1>>^(binomial(2*n, n)/(n+1)))[1, 2]:
seq(a(n), n=0..8);  # Alois P. Heinz, Jan 20 2017

Mathematica
```
Fibonacci[CatalanNumber[Range[0, 7]]]
```

for(n=0,7, cn=binomial(2*n, n)/(n+1); print1(fibonacci(cn) ","))

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

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

Original entry on oeis.org

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

Offset: 0

Waldemar Puszkarz, May 21 2016

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).

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

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

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

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

CatalanNumber[Fibonacci[Range[0,12]]]
Table[CatalanNumber[Fibonacci[n]], {n, 0,12}]

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

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

cp's OEIS Frontend

A273397 a(n) = Fibonacci(Catalan(n)).

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