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 A241421 #29 Mar 19 2025 14:31:08
%S A241421 2,2,3,5,8,8,5,5,9,5,5,0,8,9,6,9,8,6,4,2,8,3,9,6,4,7,9,9,3,1,1,8,9,0,
%T A241421 6,4,4,8,4,5,1,5,9,1,2,2,8,5,9,5,2,4,7,4,7,7,9,3,4,4,7,9,7,8,2,6,0,6,
%U A241421 2,7,0,8,1,4,5,7,2,5,2,2,1,7,9,3,2,8,3,2,0,2,9,5,2,8,3,2,3,4,6,2,8,9,8,2
%N A241421 Decimal expansion of D(1), where D(x) is the infinite product function defined in the formula section (or in the Finch reference).
%D A241421 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin Constant, p. 136.
%H A241421 G. C. Greubel, <a href="/A241421/b241421.txt">Table of n, a(n) for n = 1..5000</a>
%H A241421 L. Almodovar, V. H. Moll, H. Quand, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Moll/moll3.html">Infinite products arising in paperfolding</a>, JIS 19 (2016) # 16.5.1 eq. (15).
%H A241421 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 20.
%H A241421 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H A241421 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>
%F A241421 D(x) = lim_{n->infinity} ( Product_{k=1..2n+1} (1+x/k)^((-1)^(k+1)*k) ).
%F A241421 D(x) = (e^(x/2-1/4)*A^3*G((x+1)/2)^2*Gamma(x/2)^(x-2)*Gamma((x+1)/2)^(1-x)*(Gamma((x+1)/2)/Gamma(x/2))^x)/(2^(1/12)*G(x/2)^2), where A is the Glaisher-Kinkelin constant and G is the Barnes G-function.
%F A241421 D(1) = A^6/(2^(1/6)*sqrt(Pi)).
%e A241421 2.23588559550896986428396479931189064484515912285952474779344797826...
%t A241421 RealDigits[Glaisher^6/(2^(1/6)*Sqrt[Pi]), 10, 104] // First
%o A241421 (PARI) default(realprecision, 100); A=exp(1/12-zeta'(-1)); A^6/(2^(1/6)* sqrt(Pi)) \\ _G. C. Greubel_, Aug 24 2018
%Y A241421 Cf. A006752, A019610 (D(2)), A074962, A241420 (D(1/2)).
%K A241421 nonn,cons,easy
%O A241421 1,1
%A A241421 _Jean-François Alcover_, Aug 08 2014