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 A366022 #5 Sep 26 2023 09:32:49
%S A366022 4,8,9,6,3,5,2,2,6,6,8,4,3,0,3,3,7,3,0,8,1,5,4,1,6,6,0,5,7,8,4,6,8,6,
%T A366022 1,9,3,2,2,4,1,6,6,2,5,1,0,1,1,5,8,7,8,4,5,4,9,4,0,6,7,2,9,9,7,0,5,7,
%U A366022 5,8,4,1,5,7,1,4,0,1,6,8,3,2,8,8,7,0,5,2,2,9,0,1,9,6,3,9,3,8,9,9,1,7,3,2,7,6
%N A366022 Decimal expansion of a constant related to the asymptotics of A109085.
%F A366022 Equals limit_{n->infinity} A109085(n) * n^(3/2) / A270915^n.
%e A366022 0.489635226684303373081541660578468619322416625...
%t A366022 val = -s*Log[r*s] / Sqrt[2*Pi*((-2 - 3*Log[r*s] + 2*Log[1 - r*s])* QPolyGamma[0, 1, r*s] + QPolyGamma[0, 1, r*s]^2 - 4*ArcTanh[1 - 2*r*s]*(Log[r*s] - Log[1 - r*s]/2 - r*(s/(1 - r*s))) - 2*(Log[1 - r*s]/(1 - r*s)) - QPolyGamma[1, 1, r*s] + r*s*Log[r* s]*((-r)*s^2*Log[r*s]* Derivative[0, 2][QPochhammer][r*s, r*s] + 2*Derivative[0, 0, 1][QPolyGamma][0, 1, r*s]))] /. FindRoot[{s == 1/QPochhammer[r*s], 1/s + r*s*Derivative[0, 1][QPochhammer][r*s, r*s] == (Log[1 - r*s] + QPolyGamma[0, 1, r*s])/(s* Log[r*s])}, {r, 1/5}, {s, 1}, WorkingPrecision -> 1000]; RealDigits[Chop[val], 10, -Floor[Log[10, Abs[Im[val]]]] - 3][[1]]
%Y A366022 Cf. A109085, A270915, A366018.
%K A366022 nonn,cons
%O A366022 0,1
%A A366022 _Vaclav Kotesovec_, Sep 26 2023