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A295703
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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).
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0
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1, -1, 2, -3, 2, 4, -18, 43, -80, 123, -148, 78, 287, -1364, 3858, -8627, 15901, -23076, 20061, 18294, -140623, 420241, -930040, 1655753, -2293975, 1872682, 1835066, -12983537, 37871888, -83222132, 149287250, -212064236, 186932259, 131172644, -1139053896, 3449157957, -7710640256
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OFFSET
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0,3
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LINKS
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FORMULA
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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.
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MATHEMATICA
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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]
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}]
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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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