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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 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

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