  Lascoux, Leclerc and Thibon\cite{LLT} introduced a family of symmetric
polynomials, called LLT polynomials. We prove a $q$-multinomial expansion of
the coefficients of LLT polynomials in the case where $ \boldsymbol{\mu} =
\underbrace{(\mu,...,\mu)}_{n}$ and define a $q$-analog of a sum of the
plethysm multiplicities.
