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A084210
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G.f. A(x) defined by: A(x)^10 consists entirely of integer coefficients between 1 and 10 (A083950); A(x) is the unique power series solution with A(0)=1.
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2
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1, 1, -4, 25, -173, 1292, -10105, 81565, -673691, 5662878, -48263038, 415950272, -3617999891, 31714089336, -279828926113, 2483097203637, -22143011361045, 198317403322755
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OFFSET
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0,3
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COMMENTS
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Limit a(n)/a(n+1) --> r = -0.104430987675729 where A(r)=0.
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LINKS
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MATHEMATICA
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kmax = 20;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^10 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 10, a[k - 1], Integers] // ToRules];
coes = coes /. r, {k, 3, kmax + 1}];
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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