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A100220 Decimal expansion of Product_{k>=1} (1-1/3^k). 26

%I

%S 5,6,0,1,2,6,0,7,7,9,2,7,9,4,8,9,4,4,9,6,9,7,9,2,2,4,3,3,1,4,1,4,0,0,

%T 1,4,3,7,9,7,3,6,3,3,3,7,9,8,3,6,2,4,6,4,4,6,2,9,5,6,2,9,7,3,1,7,5,3,

%U 3,9,6,3,0,8,9,0,3,3,7,9,4,7,0,7,7,1,6,9,1,8,7,7,0,5,3,6,7,4,3,3,4,8

%N Decimal expansion of Product_{k>=1} (1-1/3^k).

%C 0.560126077... = limit of the probability that a random N X N matrix, with entries chosen independently and uniformly from the field F_3, is nonsingular [Morrison (2006)]. - _L. Edson Jeffery_, Jan 22 2012

%H G. C. Greubel, <a href="/A100220/b100220.txt">Table of n, a(n) for n = 0..1200</a>

%H Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InfiniteProduct.html">Infinite Product</a>

%F exp(-sum{k>0, sigma_1(k)/k/3^k})=exp(-sum{k>0, A000203(k)/k/3^k}). - _Hieronymus Fischer_, Aug 07 2007

%F Product_{k >=1} (1-1/3^k) = (1/3; 1/3)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - _G. C. Greubel_, Nov 27 2015

%e 0.560126077...

%t (3^(1/24)*EllipticThetaPrime[1, 0, 1/Sqrt[3]]^(1/3))/2^(1/3).

%t N[QPochhammer[1/3,1/3]] (* _G. C. Greubel_, Nov 27 2015 *)

%Y Cf. A048651, A027871.

%Y Cf. A000203, A100221, A100222, A132019, A132034, A132035, A132036, A132037, A132038, A258458.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Nov 09 2004

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)