  We present the first general formulas for the central and non-central moments
of the multinomial distribution, using a combinatorial argument and the
factorial moments previously obtained in Mosimann (1962). We use the formulas
to give explicit expressions for all the non-central moments up to order 8 and
all the central moments up to order 4. These results expand significantly on
those in Newcomer (2008) and Newcomer et al. (2008), where the non-central
moments were calculated up to order 4.
