Gaussian Integrals of Powers of Complementary Error Function

Question

Can anyone help me with the following integral: $$ \int_{-\infty}^\infty dt \frac{\exp\left\{-t^2/2\right\}}{\sqrt{2\pi}} \left(\frac{1}{2}\text{erfc}\left\{\frac{a-bt}{\sqrt{2}}\right\}\right)^n, $$ where erfc is the complementary error function, $n$ is any positive integer, $a$ & $b$ can be any real number (the special case where $b =1$ is trivial...)? Many thanks in advance