Recurrence relation of coeeficients of power series solution to DE

Question

Say I have a DE

$$ -\phi \left(\phi \left(\left(6975 \phi ^2-3704 \phi +160\right) \omega '(\phi )+\phi \left(\left(6975 \phi ^2-4688 \phi +266\right) \omega ''(\phi )+\phi \left(2 \left(675 \phi ^2-518 \phi +32\right) \omega ^{(3)}(\phi )-\phi \omega ^{(4)}(\phi )\right)\right)\right)\right) = 0 $$

and I want a recurrence relation for coefficients of a power series solution, such that the constant term $\omega(0)=1$, how can I do that?

I will change symbols to $t$ and $f$ because they will look nicer here

t[f_] := x D[f,x]
R[x_] := -9 x^3 + 5 x^2 - 4 x
L[f_,x_] := R[x] Nest[t,f,4] + R[x]^2 Nest[t,f,3] + f
diffEqn = Expand[L[h[x],x]]