# 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.

• Are you looking for a closed form of the sum? Because wolfram alpha's is kind of ugly... – recursive recursion Jan 18 '15 at 19:36
• Yes a general formula for integer n – UNM Jan 18 '15 at 19:40
• I'd go with induction here. – barak manos Jan 18 '15 at 19:48
• Please write your steps – UNM Jan 18 '15 at 19:49

Find the coefficient of $x^{0}$ in $\displaystyle (1+x)+\frac{(1+x)^{4}}{x}+\frac{(1+x)^{7}}{x^{2}}+\ldots$