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 A293238 #39 Apr 05 2025 13:03:34
%S A293238 7,1,7,7,7,0,0,1,1,0,4,6,1,2,9,9,9,7,8,2,1,1,9,3,2,2,3,6,6,5,7,7,9,4,
%T A293238 2,6,6,5,7,1,2,9,8,8,9,3,3,9,9,8,4,3,7,1,9,8,9,7,6,3,6,6,3,8,7,7,2,6,
%U A293238 9,4,2,3,1,2,5,8,4,9,8,6,6,3,7,0,1,6,1
%N A293238 Decimal expansion of the escape probability for a random walk on the 3D bcc lattice.
%C A293238 The return probability equals unity minus this constant. The expected number of visits to the origin is the inverse of this constant, A091670.
%H A293238 G. C. Greubel, <a href="/A293238/b293238.txt">Table of n, a(n) for n = 0..10000</a>
%H A293238 Shunya Ishioka and Masahiro Koiwa, <a href="https://doi.org/10.1080/01418617808239187">Random walks on diamond and hexagonal close packed lattices</a>, Phil. Mag. A, 37 (1978), 517-533.
%H A293238 G. L. Montet, <a href="https://doi.org/10.1103/PhysRevB.7.650">Integral methods in the calculation of correlation factors in diffusion</a>, Phys. Rev. B 7 (1973), 650-662.
%H A293238 <a href="/index/Ba#Bcc">Index entries for sequences related to b.c.c. lattice</a>.
%H A293238 <a href="/index/Wa#WALKS">Index entries for sequences related to walks</a>.
%F A293238 Equals Pi^2/(4*K(1/sqrt(2))^2), where K is the complete elliptic integral of the first kind.
%F A293238 Equals (4*Pi^3)/Gamma(1/4)^4. - _G. C. Greubel_, Oct 26 2018
%F A293238 Equals Product_{n>=1} exp(beta(2n)/n), where beta(n) is the Dirichlet beta function. - _Antonio Graciá Llorente_, Apr 03 2025
%F A293238 Equals Gamma(3/4)^4/Pi. - _Stefano Spezia_, Apr 05 2025
%e A293238 0.7177700110461299978211932236657794...
%t A293238 RealDigits[(4*Pi^3)/Gamma[1/4]^4, 10, 100][[1]] (* _G. C. Greubel_, Oct 26 2018 *)
%o A293238 (PARI) default(realprecision, 100); (4*Pi^3)/gamma(1/4)^4 \\ _G. C. Greubel_, Oct 26 2018
%o A293238 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (4*Pi(R)^3)/Gamma(1/4)^4; // _G. C. Greubel_, Oct 26 2018
%Y A293238 Cf. A091670, A242761, A293237.
%K A293238 nonn,cons
%O A293238 0,1
%A A293238 _Andrey Zabolotskiy_, Oct 03 2017