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Using recurrences gotten from the Apagodu-Zeilberger MultivariateAlmkvist-Zeilberger algorithm we present a linear-time, and constant-space,algorithm to compute the general mixed moments of the k-variate general normaldistribution, with any covariance matrix, for any specific k. Besides theirobvious importance in statistics, these numbers are also very significant inenumerative combinatorics, since they count in how many ways, in a species withk different genders, a bunch of individuals can all get married, keeping trackof the different kinds of heterosexual marriages. We completely implement ouralgorithm (with an accompanying Maple package, MVNM.txt) for the bivariate andtrivariate cases (and hence taking care of our own 2-sex society and a putative3-sex society), but alas, the actual recurrences for larger k took too long forus to compute. We leave them as computational challenges.

A Linear Time, and Constant Space, Algorithm to Compute the Mixed Moments of the Multivariate Normal Distributions