The coefficient of t^4 in the expansion of (1-t^61-t)^3 is:

Question

The coefficient of $t^4$ in the expansion of $\left(\dfrac{1-t^6}{1-t}\right)^3$ is:

Accepted Answer

$$\left(\frac{1-t^6}{1-t}\right)^3=(1-t^6)^3(1-t)^{-3}=(1-3t^6+3t^{12}-t^{18})\left[1+3t+6t^2+10t^3+15t^4+\cdots\right]$$

Coefficient of $t^4$ (only from the constant $1$ times the $t^4$ term of the expansion): $\dbinom{3+3}{3}$-style coefficient $=15$.

Solutions · 1