2. The coefficient of $x^{150}$ in the expansion of $\left(1+x+x^{2}+\cdots+x^{100}\right)^{3}$, after combining like terms, is $\qquad$
$\qquad$ . (Answer with a number)
2. 7651 Detailed Explanation: According to the polynomial multiplication rule, the problem can be transformed into finding the number of natural number solutions of the equation $s+t+r=150$. (1) that do not exceed 100. Clearly, the number of natural number solutions of equation (1) is $C_{152}^{2}$.

Next, we find the number of natural number solutions of equation (1) that exceed 100. Since their sum is 150, there can only be one number greater than 100, let's assume $s>100$. Transform equation (1) into $(s-101)+t+r=49$, and let $s^{\prime}=s-101$, then the number of natural number solutions of the equation $s^{\prime}+t+r=49$ is $C_{51}^{2}$. Therefore, the coefficient of $x^{150}$ is $C_{152}^{2}-C_{3}^{1} C_{51}^{2}=7651$.