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

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?

• Cauchy products? – Simply Beautiful Art Jun 10 '17 at 17:16
• $a,b\in\mathbb N$? – Simply Beautiful Art Jun 10 '17 at 17:25
• Sorry, the notification wasn't updated properly. Yes, $a, b$ are natural numbers, starting from $0$. – programmer101 Jun 10 '17 at 17:28