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

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

Offset

0,4

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).

Links

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

Formula

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

Example

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

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]]]

Prog

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

Crossrefs

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

Sequence in context: A278364 A214008 A208094 * A261433 A206386 A198902

Adjacent sequences: A273394 A273395 A273396 * A273398 A273399 A273400

Keyword

nonn,easy

Author

Waldemar Puszkarz, May 21 2016

Status

approved