How to find the coefficient of $x^n$ in $\sinh^a x\cdot \cosh^b x \cdot e^{cx}$ at $x=0$

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As the title shows, I'm looking to find the coefficient of $x^n$ in $$\sinh^a x\cdot \cosh^b x \cdot e^{cx}$$ at $x=0$, as a follow-up to this question. Expressing the hyperbolic functions in terms of $e^x$ and $e^{-x}$ doesn't do much to simplify the question.

Maybe I'm missing something, but perhaps this closed form is too complicated to be found?