[seqfan] Re: Number of hierarchical polynomial models on n factors

[N. J. A. Sloane]

Paul, I think the question is the following:

We are counting polynomials in n variables x_1 thru x_n
The total degree is bounded by k (say)

We don't care what the coeffients are

All we care about is that if the
polynomial contains a monomial
x_1^e_1*x_2^e_2*...*x_n^e_n,
then it also contains every monomial
x_1^i_1*x_2^i_2*...*x_n^i_n
for all 0 <= i_j <= e_j

It should not be hard to work out a formula
as a function of k and n

Neil