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A003266
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Product of first n nonzero Fibonacci numbers F(1), ..., F(n).
(Formerly M1692)
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30
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1, 1, 2, 6, 30, 240, 3120, 65520, 2227680, 122522400, 10904493600, 1570247078400, 365867569267200, 137932073613734400, 84138564904377984000, 83044763560621070208000, 132622487406311849122176000, 342696507457909818131702784000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Equals right border of unsigned triangle A158472 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009]
Three closely related sequences are A194157 (product of first n nonzero F(2*n)), A194158 (product of first n nonzero F(2*n-1)) and A123029 (a(2*n) = A194157(n) and a(2*n-1) = A194158(n)) [Johannes W. Meijer, Aug 21 2011]
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REFERENCES
| A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 69.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, second edition, Addison Wesley, p 597
Y. V. Matiyasevich and R. K. Guy, A new formula for pi, Amer. Math. Monthly 93 (1986), no. 8, 631-635. Math. Rev. 2000i:11199.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..50
Eric Weisstein's World of Mathematics, Fibonorial
Index to divisibility sequences
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FORMULA
| a(n) is asymptotic to C*phi^(n*(n+1)/2)/sqrt(5)^n where phi=(1+sqrt(5))/2 is the golden ratio and the decimal expansion of C is given in A062073. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 11 2003 Ben
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MAPLE
| with(combinat): A003266 := n-> mul(fibonacci(i), i=1..n): seq(A003266(n), n=1..18);
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MATHEMATICA
| a={}; s=1; Do[f=Fibonacci[n]; s=s*f; AppendTo[a, s], {n, 1, 15, 1}]; a (Vladimir Orlovsky, Jul 21 2008)
Rest[FoldList[Times, 1, Fibonacci[Range[20]]]] (* From Harvey P. Dale, Jul 11 2011 *)
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PROG
| (PARI) a(n)=prod(i=1, n, fibonacci(i)) \\ Charles R Greathouse IV, Jan 13 2012
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CROSSREFS
| Cf. A000045.
A158472 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009]
Cf. A123741 (for Fibonacci second version), A002110 (for primes), A070825 (for Lucas), A003046 (for Catalan), A126772 (for Padovan), A069777 (q-factorial numbers for sums of powers). [Johannes W. Meijer, Aug 21 2011]
Sequence in context: A089459 A027882 A106209 * A097385 A066068 A121406
Adjacent sequences: A003263 A003264 A003265 * A003267 A003268 A003269
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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