The coefficient of $$x^7$$ in $$(1 - x + 2x^3)^{10}$$ is _______.

Find coefficient of $$x^7$$ in $$(1 - x + 2x^3)^{10}$$.

Using multinomial expansion: $$(1 - x + 2x^3)^{10} = \sum \frac{10!}{a!b!c!}(1)^a(-x)^b(2x^3)^c$$

where $$a + b + c = 10$$ and $$b + 3c = 7$$.

From $$b + 3c = 7$$: possible $$(c, b) = (0,7), (1,4), (2,1)$$

Case 1: $$c=0, b=7, a=3$$: $$\frac{10!}{3!7!0!}(-1)^7 = -120$$

Case 2: $$c=1, b=4, a=5$$: $$\frac{10!}{5!4!1!}(-1)^4 \cdot 2 = \frac{10!}{5!4!} \cdot 2 = 1260 \times 2 = 2520$$. Wait: $$\frac{10!}{5!4!1!} = \frac{3628800}{120 \cdot 24} = 1260$$. So $$1260 \times 2 = 2520$$.

Case 3: $$c=2, b=1, a=7$$: $$\frac{10!}{7!1!2!}(-1)^1 \cdot 4 = -\frac{10!}{7!2!} \times 4 = -360 \times 4$$. $$\frac{10!}{7!2!} = \frac{3628800}{5040 \times 2} = 360$$. So $$-360 \times 4 = -1440$$.

Total = $$-120 + 2520 - 1440 = 960$$

The answer is 960.