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%I #30 Nov 29 2017 15:50:49
%S 1,-1,2,-3,2,4,-18,43,-80,123,-148,78,287,-1364,3858,-8627,15901,
%T -23076,20061,18294,-140623,420241,-930040,1655753,-2293975,1872682,
%U 1835066,-12983537,37871888,-83222132,149287250,-212064236,186932259,131172644,-1139053896,3449157957,-7710640256
%N Expansion of R(x*R(x)), where R(x) = 1/(1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + ...))))), a continued fraction (g.f. for A007325).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>
%F G.f.: 1/(1 + x/(1 + x/(1 + x^2/(1 + x^3/(1 + ...))))/(1 + x^2/(1 + x/(1 + x^2/(1 + x^3/(1 + ...))))^2/(1 + x^3/(1 + x/(1 + x^2/(1 + x^3/(1 + ...))))^3/(1 + ...)))), a continued fraction.
%t nmax = 36; CoefficientList[Series[1/(1 + ContinuedFractionK[(x/(1 + ContinuedFractionK[x^k, 1, {k, 1, nmax}]))^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
%t g[x_] := g[x] = QPochhammer[x, x^5] QPochhammer[x^4, x^5]/(QPochhammer[x^2, x^5] QPochhammer[x^3, x^5]); a[n_] := a[n] = SeriesCoefficient[g[x g[x]], {x, 0, n}]; Table[a[n], {n, 0, 36}]
%Y Cf. A003823, A007325, A055101, A055102, A055103, A127632, A286509, A291651.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Nov 29 2017
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