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 A118292 Decimal expansion of (Gamma(1/6)*Gamma(1/3))/(3*sqrt(Pi)). 5
 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; text; internal format)
 OFFSET 1,1 COMMENTS General formula: Integral_{x=0..1} (1+x^(3n))/sqrt(1-x^3) dx = 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. - Artur Jasinski gamma(1/6)*gamma(1/3)/(3*sqrt(Pi)) = gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi). - Harry J. Smith, May 09 2009 LINKS Harry J. Smith, Table of n, a(n) for n = 1..4000 Eric Weisstein's World of Mathematics, Butterfly Curve FORMULA Equals A073005^3 / (A002194*A002580*A000796) [see Vidunas, arXiv:math.CA/0403510]. - R. J. Mathar, Nov 30 2008 EXAMPLE 2.8043642106509085223500381581005882709260444108... - Harry J. Smith, May 09 2009 MATHEMATICA RealDigits[(Gamma[1/3]^3)/(2^(1/3) Sqrt[3] Pi), 10, 200] (* Artur Jasinski*) 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)); } \\ Harry J. Smith, Jun 20 2009 CROSSREFS Cf. A146752, A146753 Cf. A160323 (continued fraction). - Harry J. Smith, May 09 2009 Sequence in context: A021785 A136664 A086728 * A160584 A191334 A251794 Adjacent sequences:  A118289 A118290 A118291 * A118293 A118294 A118295 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Apr 22 2006 EXTENSIONS Edited by N. J. A. Sloane, Nov 16 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified December 9 17:51 EST 2018. Contains 318023 sequences. (Running on oeis4.)