

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
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OFFSET

1,1


COMMENTS

General formula: Integral_{x=0..1} (1+x^(3n))/sqrt(1x^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=(xd)*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



