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In the absence of additional information about the form, and just eyeballing the shape makes it look like a rational polynomial-ish thing, I vote for...

nlf = NonlinearModelFit[data, (c0 + c1 x + c2 x^2)/(c3 + c4 x + x^c5), {c0, c1, c2, c3, c4, c5}, x];

$ \frac{-2.10241 x^2-1735.16 x-43612.1}{x^{2.25431}+116.08 x+1843.92} $

 nlf["FitResiduals"] // MinMax


{-0.0134303, 0.014954}

 Plot[nlf[x], {x, 1, 300}, Epilog -> Point[data]]

enter image description here