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A273397 a(n) = Fibonacci(Catalan(n)). 3
1, 1, 1, 5, 377, 267914296, 1725375039079340637797070384, 202401005213503038261932567177107618332887918916819829782797456368284639448671475316218754 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Waldemar Puszkarz, May 21 2016
STATUS
approved

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Last modified May 27 14:41 EDT 2024. Contains 372861 sequences. (Running on oeis4.)