A084209 - OEIS

%I #6 Jul 26 2018 18:43:51

%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[k-1], Integers] // ToRules];

%t coes = coes /. r, {k, 3, kmax + 1}];

%t Table[a[k], {k, 0, kmax}] /. r (* _Jean-François Alcover_, Jul 26 2018 *)

%Y Cf. A083949, A084202-A084208, A084210-A084212.

%K sign

%O 0,3

%A _Paul D. Hanna_, May 20 2003