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A282045
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Coefficients in solution to a certain functional equation.
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1
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1, 12, 168, 2496, 38328, 600672, 9539808, 152891520, 2466138552, 39966566304, 650017375488, 10601365433088, 173287953476448, 2837739346914432, 46542227947686912, 764357417859726336, 12567429586754388408, 206842036732301620896, 3407427981753822944448
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f. f(z) satisfies f(z/(1+mu*z)^3) / (1+mu*z)^2 = f(z^2/(1+lambda*z)^3) / (1+lambda*z)^2 with mu=2, lambda=-4.
a(n) = Sum_{0<=k<=n} A282046(k)*A282046(n-k), i.e., this is a convolution transform of A282046. Hence f(z)=g(z)^2, where g(z) is the g.f. of A282046.
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MATHEMATICA
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terms=19; f[_]=1; Do[f[z_] = f[z]-f[z/(1+2z)^3] / (1+2z)^2+f[z^2/(1-4z)^3]/ (1-4z)^2 + O[z]^terms // Normal, {terms}]; f[z] // CoefficientList[#, z]& (* Jean-François Alcover, Oct 10 2018, after Andrey Zabolotskiy *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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