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 A086308 #33 Feb 16 2025 08:32:50
%S A086308 5,3,4,9,4,9,6,0,6,1,4,2,3,0,7,0,1,4,5,5,0,3,7,9,7,1,1,0,5,2,0,6,8,3,
%T A086308 9,8,1,4,3,1,1,6,5,1,4,0,5,6,9,9,0,0,9,3,9,7,7,0,7,6,8,1,0,2,3,7,5,2,
%U A086308 3,2,1,7,8,8,0,6,4,0,6,7,2,3,9,7,8,3,2,6,2,2,4,1,8,5,9,1,1,0,4,4,4,6,6,9,3,7
%N A086308 Decimal expansion of Otter's asymptotic constant beta for the number of unrooted trees.
%C A086308 A000055(n) ~ 0.5349496061 * alpha^n * n^(-5/2), where alpha = 2.95576528565199497... (see A051491). - _Vaclav Kotesovec_, Jan 04 2013
%D A086308 Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6., p. 296.
%H A086308 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Tree.html">Tree</a>
%e A086308 0.53494960614230701455037971105206839814311651405699...
%t A086308 digits = 86; max = 250; s[n_, k_] := s[n, k] = a[n+1-k] + If[n < 2*k, 0, s[n-k, k]]; a[1] = 1; a[n_] := a[n] = Sum[a[k]*s[n-1, k]*k, {k, 1, n-1}]/(n-1); A[x_] := Sum[a[k]*x^k, {k, 0, max}]; APrime[x_] := Sum[k*a[k]*x^(k-1), {k, 0, max}]; eq = Log[c] == 1 + Sum[A[c^-k]/k, {k, 2, max}]; alpha = c /. FindRoot[eq, {c, 3}, WorkingPrecision -> digits+5]; b = Sqrt[(1+Sum[APrime[alpha^-k]/alpha^k, {k, 2, max}])/(2*Pi)]; beta = 2*Pi*b^3; RealDigits[beta, 10, digits] // First (* _Jean-François Alcover_, Sep 24 2014 *)
%Y A086308 Cf. A000055, A000081, A051491, A187770.
%K A086308 nonn,cons
%O A086308 0,1
%A A086308 _Eric W. Weisstein_, Jul 15 2003
%E A086308 Corrected and extended by _Vaclav Kotesovec_, Jan 04 2013
%E A086308 More terms from _Vaclav Kotesovec_, Jun 20 2013 and Dec 26 2020