Question about A006906

[N. J. A. Sloane]

seems to want to be 1. So I am
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From: "David W. Cantrell" <DWCantrell at sigmaxi.net>
To: <njas at research.att.com>, "Sequence Fans" <seqfan at ext.jussieu.fr>,
   "David Wilson" <davidwwilson at comcast.net>
References: <200705191142.l4JBgDaN13378105 at fry.research.att.com>
Subject: Re: Question about A006906
Date: Sat, 19 May 2007 14:11:26 +0100
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> David is right, strictly speaking, since
> there are no terms.

No. That would have been correct if the entry had concerned the sum of 
terms in all partitions of n, for then we would have the empty sum, 
namely, 0. But instead, the entry concerned the sum of _products_ of 
terms.

As Max A. already noted, the only partition of 0 is the empty 
partition. The product of its terms is the empty product, namely, 1. 
Therefore, a(0) = 1.

> But the leading term
> seems to want to be 1. So I am
> changing the definition to:
> %N A006906 a(0) = 1; for n >=1, a(n) = sum of products of terms in 
> all partitions of n.

I hope you won't change the definition. Doing so would be a needless 
complication.

David Cantrell

>> Shouldn't A006906(0) = 0 ?