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

Paul D Hanna pauldhanna at juno.com
Wed Feb 8 20:23:14 CET 2012

     Please see the email (below) I just received. 
Question appears to be regarding a generalization of 
A006898(n) = Sum_{k=0..n} C(n,k)*2^(k*(k+1)/2). 
Could someone shed some light on the subject? 
---------- Original Message ----------
From: viallon at math.univ-lyon1.fr
To: pauldhanna at juno.com
Subject: Number of hierarchical polynomial models on n factors
Date: Wed, 08 Feb 2012 15:12:09 +0100

Dear Professor,

I'm a French statistician (so please excuse my English) and I'm trying  
to compute the number of hierarchical polynomial models on n factors,  
that is, a generalization of the number of hierarchical quadratic  
models on n factors, where instead of considering only interaction of  
order 1, typically, Xi*Xj, we would consider interaction of order, say  
k, (for instance X1*X2*...*Xk).

Would you know any such result (or approximation)?

Thanks in advance for your time.

Best wishes

Vivian V.

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