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A062073
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Decimal expansion of Fibonacci factorial constant.
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9
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1, 2, 2, 6, 7, 4, 2, 0, 1, 0, 7, 2, 0, 3, 5, 3, 2, 4, 4, 4, 1, 7, 6, 3, 0, 2, 3, 0, 4, 5, 5, 3, 6, 1, 6, 5, 5, 8, 7, 1, 4, 0, 9, 6, 9, 0, 4, 4, 0, 2, 5, 0, 4, 1, 9, 6, 4, 3, 2, 9, 7, 3, 0, 1, 2, 1, 4, 0, 2, 2, 1, 3, 8, 3, 1, 5, 3, 1, 2, 1, 6, 8, 4, 5, 2, 6, 2, 1, 5, 6, 2, 4, 9, 4, 7, 9, 7, 7, 4, 1, 2, 5, 9, 1, 3
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The Fibonacci factorial constant is associated with the Fibonacci factorial A003266.
Two closely related constants are A194159 and A194160. [Johannes W. Meijer, Aug 21 2011]
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REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.5.
R. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison Wesley, 1990, pp. 478, 571.
M. Griffiths, Symmetric rational expressions ..., Fib. Q., 46/47 (2008/2009), 262-267. [From N. J. A. Sloane, Dec 05 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,5000
Simon Plouffe, Plouffe's Inverter
Eric Weisstein's World of Mathematics, Fibonacci Factorial Constant
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FORMULA
| C = (1-a)*(1-a^2)*(1-a^3)... 1.2267420... where a = -1/phi^2 and where phi is the Golden ratio = 1/2 + sqrt(5)/2.
C = QPochhammer[ -1/GoldenRatio^2] [From Eric W. Weisstein (eric(AT)weisstein.com), Dec 01 2009]
C = A194159 * A194160 [Johannes W. Meijer, Aug 21 2011]
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EXAMPLE
| 1.2267420107203532444176302...
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MATHEMATICA
| RealDigits[N[QPochhammer[-1/GoldenRatio^2], 105]][[1]](* From Alonso del Arte, alonso.delarte(AT)gmail.com, Dec 20 2010 *)
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PROG
| (PARI) \p 1300 a=-1/(1/2+sqrt(5)/2)^2; prod(n=1, 17000, (1-a^n))
(PARI) { default(realprecision, 5080); p=-1/(1/2 + sqrt(5)/2)^2; x=prodinf(k=1, 1-p^k); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b062073.txt", n, " ", d)) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 31 2009]
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CROSSREFS
| Cf. A062072.
Sequence in context: A056038 A076929 A174789 * A021445 A011145 A177852
Adjacent sequences: A062070 A062071 A062072 * A062074 A062075 A062076
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KEYWORD
| easy,nonn,cons
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jun 27 2001
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