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%I #19 Jul 17 2017 02:26:47
%S 1,1,2,4,9,20,45,101,228,514,1160,2617,5906,13327,30075,67868,153156,
%T 345621,779953,1760094,3971951,8963378,20227382,45646511,103009086,
%U 232457449,524579615,1183802763,2671451479,6028582814,13604518396,30700900429,69281782713
%N G.f. A(x) = 1 / (1 - x^a(0) / (1 - x^a(1) / (1 - x^a(2) / ... ))).
%e 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 45*x^6 + 101*x^7 + 228*x^8 + ...
%t terms = 29; f[k_] := If[k >= 0, -x^a[k], 1]; F[m_] := ContinuedFractionK[ f[k], 1, {k, -1, m}]; s[0] = {a[0] -> 1}; eq[n_] := eq[n] = Normal[( F[n-1] /. s[n-1]) + O[x]^(n+1)] - Sum[a[k] x^k, {k, 0, n}] == 0 /. s[n-1]; s[n_] := s[n] = Join[s[n-1], SolveAlways[eq[n], x] [[1]]]; Reap[ Do[ Print["a(", n, ") = ", an = a[n] /. s[n]]; Sow[an], {n, 0, terms-1} ]][[2, 1]] (* _Jean-François Alcover_, Jul 16 2017 *)
%K nonn,nice
%O 0,3
%A _Michael Somos_, Jun 10 2012
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