Simple Combinations Binomial There is a little sum I am stuck with.

Find the value of
$${1 \choose 0}+{4 \choose 1}+{7 \choose 2} +\ldots+{3n+1 \choose n}$$

where ${n \choose r}$ is the usual combination.

A little hint will be fine.
Find the coefficient of $x^{0}$ in $\displaystyle  (1+x)+\frac{(1+x)^{4}}{x}+\frac{(1+x)^{7}}{x^{2}}+\ldots$
It's forming a geometric series.
Find the coefficient of $x^{0}$ in $\displaystyle  (1+x)+\frac{(1+x)^{4}}{x}+\frac{(1+x)^{7}}{x^{2}}+\ldots$
It's forming a geometric series.