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Indeed, python functions like Df do not like to be added to integers like n-1, or multiplied together.

Is there a reason not to do the computation in a single step ?

sage: var('t z')
sage: f = z*t*exp(t/z)
sage: prod([ t*f.derivative(t) - n-1 for n in range(5) ])
((t*e^(t/z) + z*e^(t/z))*t - 1)*((t*e^(t/z) + z*e^(t/z))*t - 2)*((t*e^(t/z) + z*e^(t/z))*t - 3)*((t*e^(t/z) + z*e^(t/z))*t - 4)*((t*e^(t/z) + z*e^(t/z))*t - 5)