cp's OEIS Frontend

A272192 Decimal expansion of the radius of convergence of the generating function of A000625 (alcohol stereoisomers enumeration).

%I A272192 #9 Apr 24 2016 05:22:47
%S A272192 3,0,4,2,1,8,4,0,9,0,7,4,6,4,6,5,1,3,0,8,1,9,0,5,8,9,3,9,4,4,2,6,3,8,
%T A272192 1,7,5,3,4,6,7,2,3,4,9,1,4,0,9,8,5,5,2,1,2,9,0,6,7,1,2,1,8,0,0,8,0,5,
%U A272192 4,6,1,8,9,7,0,8,3,6,2,6,1,4,4,0,1,3,7,4,3,9,9,6,2,3,1,3,2,8,4,2,8,9
%N A272192 Decimal expansion of the radius of convergence of the generating function of A000625 (alcohol stereoisomers enumeration).
%C A272192 Data were computed from _Vaclav Kotesovec_'s data in A239803.
%D A272192 Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6., p. 301.
%F A272192 Equals 1 / A239803.
%e A272192 0.304218409074646513081905893944263817534672349140985521290671218...
%t A272192 (* This approximation gives 9 correct digits: *)
%t A272192 For[A = 1 + x; m = 3, m <= 10, m++, A = 1 + x/3 (A^3 + 2 (Normal[A] /. x -> x^3)) + O[x]^m];
%t A272192 A = A // Normal;
%t A272192 S0[x_] = PadeApproximant[A, {x, 0, {3, 2}}];
%t A272192 sol = S /. Solve[S == 1 + x/3 (S^3 + 2 S0[x^3]), S];
%t A272192 r = x /. FindRoot[sol[[1]] == sol[[3]], {x, 1/3}] // Chop;
%t A272192 RealDigits[r][[1]]
%Y A272192 Cf. A000625, A239803.
%K A272192 nonn,cons
%O A272192 0,1
%A A272192 _Jean-François Alcover_, Apr 22 2016