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

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

Offset: 0

Author

Waldemar Puszkarz, May 21 2016

Keywords

• nonn
• easy

Comments

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).

Examples

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

Links

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

Crossrefs

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

Programs

Maple

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]]]

PARI

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

Formula

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