How can I find the generating function of this sequence: $$(0,2,0,4,0,6,0,8,0,...)$$
I have obtained this sum $$2s(1+2s^2+3s^4+4s^6+...)$$ but not more.
I need a closed formula for the generating sequence.
EDIT Is this correct:
$$\frac{2s}{(1-s^2)^2}$$