Consider a theory for a finite number of real scalar fields $\phi _i$ with interaction terms of the form $$ -\lambda _{ijk}\phi _i\partial _\mu \phi _j\partial ^\mu \phi _k, $$ with the sum over $i,j,k$ being implicit. Without loss of generality, assume that $\lambda _{ijk}$ is symmetric in $j$ and $k$.
Consider the thee-point interaction vertex between three of these fields of type $i$, $j$, and $k$ with momenta respectively $p_1$, $p_2$, and $p_3$. I just want to check that I have the Feynman rule for this vertex correct (so I can proceed on with the rest of my computation without being unsure if my Feynman rule is even correct). I believe the Feynman rule associated to this vertex should be $$ -2\mathrm{i}\, (p_1\cdot p_2\lambda _{kij}+p_1\cdot p_3\lambda _{jik}+p_2\cdot p_3\lambda _{ijk}). $$
Is this correct?