Uses Taylor's theorem to give one over one minus a multipol

`ooom(n, a, maxorder=NULL)`

n

The order of the approximation; see details

a

A multipol

maxorder

A vector of integers giving the maximum order as per
`taylor()`

The motivation for this function is the *formal* power series
\((1-x)^{-1}=1+x+x^2+\ldots\). The way to
think about it is to observe that
\((1+x+x^2+\ldots+x^n)(1-x)=1-x^{n-1}\),
even if \(x\) is a multivariate polynomial (one needs only power
associativity and a distributivity law, so this works for
polynomials). The right hand side is \(1\) if we neglect powers of
\(x\) greater than the \(n\)-th, so the two terms on the left hand
side are multiplicative inverses of one another.

Argument `n`

specifies how many terms of the series to take.

The function uses an efficient array method when `x`

has only a single
non-zero entry. In other cases, a variant of Horner's method is
used.

I. J. Good 1976. “On the application of symmetric Dirichlet
distributions and their mixtures to contingency tables”. *The
Annals of Statistics*, volume 4, number 6, pp1159-1189; equation 5.6,
p1166

# NOT RUN { ooom(4,homog(3,1)) # How many 2x2 contingency tables of nonnegative integers with rowsums = # c(2,2) and colsums = c(2,2) are there? Good gives: ( ooom(2,lone(4,c(1,3))) * ooom(2,lone(4,c(1,4))) * ooom(2,lone(4,c(2,3))) * ooom(2,lone(4,c(2,4))) )[2,2,2,2] # easier to use the aylmer package: # } # NOT RUN { library(aylmer) no.of.boards(matrix(1,2,2)) # } # NOT RUN { # }