Laplace inverse of $e^{-as-bs^2}/(as+bs^2)$

Question

I want to know how to do the laplace inverse transform $$e^{-as-bs^2}/(as+bs^2).$$ I have tried to use convolution and any fomula I know, but I cannot deal with one part, $e^{bs^2}$. I searched internet and any laplace transform calculator, but I could not find any result about $e^{s^2}$. Is it really impossible to do the Laplace transfrom of $e^{s^2}$?