This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A100221 #45 Feb 16 2025 08:32:55
%S A100221 6,8,8,5,3,7,5,3,7,1,2,0,3,3,9,7,1,5,4,5,6,5,1,4,3,5,7,2,9,3,5,0,8,1,
%T A100221 8,4,6,7,5,5,4,9,8,1,9,3,7,8,3,3,5,7,3,5,3,4,0,1,5,7,2,3,2,5,7,7,5,3,
%U A100221 3,1,9,8,4,5,0,7,9,8,6,7,5,1,2,4,8,0,3,3,4,6,0,4,8,1,4,2,8,8,7,9,0,5
%N A100221 Decimal expansion of Product_{k>=1} (1-1/4^k).
%H A100221 G. C. Greubel, <a href="/A100221/b100221.txt">Table of n, a(n) for n = 0..1200</a>
%H A100221 Richard J. McIntosh, <a href="https://doi.org/10.1112/jlms/51.1.120">Some Asymptotic Formulae for q-Hypergeometric Series</a>, Journal of the London Mathematical Society, Vol. 51, No. 1 (1995), pp. 120-136; <a href="https://citeseerx.ist.psu.edu/pdf/4f03a5e304ec19f8a725774525aecd2a78f4ad81">alternative link</a>.
%H A100221 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InfiniteProduct.html">Infinite Product</a>.
%H A100221 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A100221 Equals exp(-Sum_{k>0} sigma_1(k)/(k*4^k)) where sigma_1() is A000203(). - _Hieronymus Fischer_, Aug 07 2007
%F A100221 Equals (1/4; 1/4)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - _G. C. Greubel_, Nov 30 2015
%F A100221 From _Amiram Eldar_, May 09 2023: (Start)
%F A100221 Equals sqrt(Pi/log(2)) * exp(log(2)/12 - Pi^2/(12*log(2))) * Product_{k>=1} (1 - exp(-2*k*Pi^2/log(2))) (McIntosh, 1995).
%F A100221 Equals Sum_{n>=0} (-1)^n/A027637(n). (End)
%e A100221 0.68853753712033971545651435729350818467554981937833...
%t A100221 EllipticThetaPrime[1, 0, 1/2]^(1/3)/2^(1/4)
%t A100221 N[QPochhammer[1/4]] (* _G. C. Greubel_, Nov 30 2015 *)
%t A100221 RealDigits[Fold[Times,1-1/4^Range[1000]],10,110][[1]] (* _Harvey P. Dale_, Sep 27 2024 *)
%o A100221 (PARI) prodinf(x=1, 1-1/4^x) \\ _Altug Alkan_, Dec 01 2015
%Y A100221 Cf. A027637, A048651, A100220, A100222.
%Y A100221 Cf. A000203, A132020, A132034, A132035, A132036, A132037, A132038, A258459.
%K A100221 nonn,cons
%O A100221 0,1
%A A100221 _Eric W. Weisstein_, Nov 09 2004