Since after re-writting my question there is still no further answer, I try to describe my question in another way.
The expression looks as follow:
y = a*(datas + Prev(datas,1)/2) + b*Prev(y,1) + c*Prev(y,2)
The a, b and c are constants.
The datas is a Series and has n-elements.
The Prev(datas,1) is the privious value of datas.
The initial values of y are 0 and can be defined as:
y = pd.Series(np.zeros_like(datas))
The Prev(y, 1) is the privious of y and the Prev(y,2) is the privious of Prev(y,1)