Does anyone know of any clever tricks that solve
$$\large G_n(t) = \int_0^t dt_1 \int_0^{t_1} dt_2 \cdots \int_0^{t_{n-2}}dt_{n-1}\int_0^{t_{n-1}}dt_{n} e^{i\lambda(t_1-t_2+t_3-\cdots + t_{n-1}-t_n)}$$
I've come up with a few recursion relations but I'm finding it hard to pin down the exact answer.