I can obtain

$\displaystyle

M_{X}(t) = e^{\mu t + \sigma^{2}t^{2}/2}

$

as the moment generating function of the normal distribution but I dont see the step to obtain

$\displaystyle

E(X^n) = e^{n \mu + \frac{1}{2}n^{2}\sigma^{2}}

$

as the Taylor series elements of the lognormal moment generating function.