I would like to calculate the power series solution of a set of ODEs. However, I know that this power series will contain non-integer coefficients, which are dependent on a (rational) parameter of the system, α. I'm solving the ODE by power series in the usual way, that is, by defining each of the solution variables as a function with the first few terms of their power series (with unknown coefficients), substituting these into the ODEs, and finding a series of the ODE which should be of the form: