A213411 G.f. A(x) = 1 / (1 - x^a(0) / (1 - x^a(1) / (1 - x^a(2) / ... ))).

1, 1, 2, 4, 9, 20, 45, 101, 228, 514, 1160, 2617, 5906, 13327, 30075, 67868, 153156, 345621, 779953, 1760094, 3971951, 8963378, 20227382, 45646511, 103009086, 232457449, 524579615, 1183802763, 2671451479, 6028582814, 13604518396, 30700900429, 69281782713

Offset: 0

Author

Michael Somos, Jun 10 2012

Keywords

• nonn
• nice

Examples

			1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 45*x^6 + 101*x^7 + 228*x^8 + ...
		

Programs

Mathematica

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 *)