A084210 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.

1, 1, -4, 25, -173, 1292, -10105, 81565, -673691, 5662878, -48263038, 415950272, -3617999891, 31714089336, -279828926113, 2483097203637, -22143011361045, 198317403322755

Offset: 0

Author

Paul D. Hanna, May 20 2003

Keywords

• sign

Comments

Limit a(n)/a(n+1) --> r = -0.104430987675729 where A(r)=0.

Crossrefs

Cf. A083950, A084202-A084209, A084211, A084212.

Programs

Mathematica

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}];
Table[a[k], {k, 0, kmax}] /. r (* Jean-François Alcover, Jul 26 2018 *)