I need to count the number of monomials of degree $n$ in $k$ variables that contain at least one variable with a power of 1, for example $x_1x_2^2x_3x_4^6$.

I need to count the number of monomials of degree $n$ in $k$ variables, $x_1,\ldots ,x_k$, that contain at least one variable with a power of 1. The monomials need not include all the variables. Their powers just need to some to $n$ and they must be divisible by $x_i$, but not $x_i^2$, for some $i$.