%I
%S 1,1,3,15,85,523,3367,22371,152104,1052568,7385756,52410754,
%T 375382683,2709626768,19688989762,143885743077,1056748051734,
%U 7795106129504,57723430872280,428923406694402
%N G.f. A(x) defined by: A(x)^9 consists entirely of integer coefficients between 1 and 9 (A083949); A(x) is the unique power series solution with A(0)=1.
%C Limit a(n)/a(n+1) > r = 0.126715878986521 where A(r)=0.
%t kmax = 20;
%t A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
%t coes = CoefficientList[A[x]^9 + O[x]^(kmax + 1), x];
%t r = {a[0] > 1, a[1] > 1};
%t coes = coes /. r;
%t Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 9, a[k1], Integers] // ToRules];
%t coes = coes /. r, {k, 3, kmax + 1}];
%t Table[a[k], {k, 0, kmax}] /. r (* _JeanFrançois Alcover_, Jul 26 2018 *)
%Y Cf. A083949, A084202A084208, A084210A084212.
%K sign
%O 0,3
%A _Paul D. Hanna_, May 20 2003
