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A118292
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Decimal expansion of (Gamma[1/6]*Gamma[1/3])/(3*Sqrt[Pi]).
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5
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2, 8, 0, 4, 3, 6, 4, 2, 1, 0, 6, 5, 0, 9, 0, 8, 5, 2, 2, 3, 5, 0, 0, 3, 8, 1, 5, 8, 1, 0, 0, 5, 8, 8, 2, 7, 0, 9, 2, 6, 0, 4, 4, 4, 1, 0, 8, 4, 7, 9, 7, 2, 1, 9, 2, 3, 6, 3, 9, 8, 7, 9, 7, 4, 1, 5, 2, 5, 6, 9, 5, 3, 1, 9, 6, 3, 6, 0, 6, 5, 9, 2, 1, 4, 1, 7, 0, 4, 5, 3, 2, 9, 7, 0, 0, 4, 9, 5, 6, 9, 4, 1, 1, 0, 3
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| General formula (*Artur Jasinski*): Integrate[(1+x^(3n))/Sqrt[1-x^3],{x,0,1}] = G_3 * k_n = G_3*A146751(n)/A146752(n) = A118292*A146751(n)/A146752(n) where G_3 = (Gamma[1/3]^3)/(2^(1/3)Sqrt[3]Pi) is the number in the present entry. For numerators of k_n see A146752, for denominators of k_n see A146753.
gamma(1/6)*gamma(1/3)/(3*sqrt(Pi)) = gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,4000
Eric Weisstein's World of Mathematics, Butterfly Curve
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FORMULA
| Equals A073005^3 / (A002194*A002580*A000796) [see Vidunas, arXiv:math.CA/0403510] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2008]
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EXAMPLE
| 2.8043642106509085223...
2.8043642106509085223500381581005882709260444108479721923639879741525695... [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
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MATHEMATICA
| RealDigits[(Gamma[1/3]^3)/(2^(1/3) Sqrt[3] Pi), 10, 200] (*Artur Jasinski*)
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PROG
| (PARI) { allocatemem(932245000); default(realprecision, 4080); x=gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi); for (n=1, 4000, d=floor(x); x=(x-d)*10; write("b118292.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 20 2009]
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CROSSREFS
| Cf. A146752, A146753
Cf. A160323 = Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
Sequence in context: A021785 A136664 A086728 * A160584 A191334 A188924
Adjacent sequences: A118289 A118290 A118291 * A118293 A118294 A118295
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KEYWORD
| nonn,cons
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 22, 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 16 2008 at the suggestion of R. J. Mathar
Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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