7. The generating function of the sequence $\left\{0^{2}, 1^{2}, 2^{2}, 3^{2}, \cdots\right\}$ is
7. $\frac{t(1+t)}{(1-t)^{3}}$ Hint: Differentiate both sides of the identity $\frac{t}{(1-t)^{2}}=t+2 t^{2}+3 t^{3}+4 t^{4}+\cdots+n t^{n}+\cdots$ to obtain the result.