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A248897 Decimal expansion of Sum_{i >= 0} (i!)^2/(2*i+1)!. 6
1, 2, 0, 9, 1, 9, 9, 5, 7, 6, 1, 5, 6, 1, 4, 5, 2, 3, 3, 7, 2, 9, 3, 8, 5, 5, 0, 5, 0, 9, 4, 7, 7, 0, 4, 8, 8, 1, 8, 9, 3, 7, 7, 4, 9, 8, 7, 2, 8, 4, 9, 3, 7, 1, 7, 0, 4, 6, 5, 8, 9, 9, 5, 6, 9, 2, 5, 4, 1, 5, 4, 5, 4, 0, 8, 4, 2, 3, 5, 9, 2, 2, 4, 5, 6, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Value of the Borwein-Borwein function I_3(a,b) for a = b = 1. - Stanislav Sykora, Apr 16 2015

LINKS

Table of n, a(n) for n=1..87.

Xavier Gourdon and Pascal Sebah, Collection of series for Pi (see paragraph 7).

Richard Kershner, The Number of Circles Covering a Set, American Journal of Mathematics, 61(3), 665-671.

László Fejes Tóth, An Inequality concerning polyhedra, Bull. Amer. Math. Soc. 54 (1948), 139-146. See (9) p. 146.

Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean, equations 26-32.

FORMULA

Equals 2*sqrt(3)*Pi/9 = 1 + 1/6 + 1/30 + 1/140 + 1/630 + 1/2772 + 1/12012 + ...

Equals m*I_3(m,m) = m*Integral[0..inf](x/(m^3+x^3)), for any m>0. - Stanislav Sykora, Apr 16 2015

Equals Integral_{x=0..infinity} (1/(1+x^3)) dx. - Robert FERREOL, Dec 23 2016

EXAMPLE

1.2091995761561452337293855050947704881893774987284937170465899569254...

MATHEMATICA

RealDigits[2 Sqrt[3] Pi/9, 10, 100][[1]]

PROG

(PARI) a = 2*Pi/(3*sqrt(3)) \\ Stanislav Sykora, Apr 16 2015

CROSSREFS

Cf. A000796, A002194, A248181, A257096, A257097, A186706.

Cf. A091682 (Sum_{i >= 0} (i!)^2/(2*i)!).

Sequence in context: A011125 A197583 A021831 * A021482 A199287 A198735

Adjacent sequences:  A248894 A248895 A248896 * A248898 A248899 A248900

KEYWORD

nonn,cons

AUTHOR

Bruno Berselli, Mar 06 2015

STATUS

approved

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Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)