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A084209
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.
2
1, 1, -3, 15, -85, 523, -3367, 22371, -152104, 1052568, -7385756, 52410754, -375382683, 2709626768, -19688989762, 143885743077, -1056748051734, 7795106129504, -57723430872280, 428923406694402
OFFSET
0,3
COMMENTS
Limit a(n)/a(n+1) --> r = -0.126715878986521 where A(r)=0.
MATHEMATICA
kmax = 20;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^9 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 9, a[k-1], Integers] // ToRules];
coes = coes /. r, {k, 3, kmax + 1}];
Table[a[k], {k, 0, kmax}] /. r (* Jean-François Alcover, Jul 26 2018 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 20 2003
STATUS
approved