$$\sum_{n=0}^{l}{{n+v \brack n+2}}$$
I know that at $v=2$, the summation above is equal to $l+1$, and at $v=3$, the summation is equal to $$\binom{l+4}{3}-1.$$ What does the summation generally evaluate to? Thanks a lot, family! The notation $\genfrac[]{0pt}{}{x}{y}$ denotes the unsigned Stirling numbers of the first kind.