Distinct monomials in a six-variable sum to the 18th

Consider the polynomial $\left(\sum_{i=1}^{6}x_i\right)^{18}$ in six variables. After multiplying out and merging like terms, how many distinct monomials does it have?

$33649$. Each term is $x_1^{e_1}\cdots x_6^{e_6}$ with non-negative integer exponents summing to $18$. By stars and bars there are $\binom{23}{5}=33649$ such exponent vectors.