[seqfan] Re: Need help with notation: sums of subset products

[Neil Sloane]

PS and so then you can say what the answer is:  if your have 4 numbers a b
c d
then look at the product (1+ax)(1+bx)(1+cx)(1+dx)
and expand it in powers of x. You want the sum of the coefficients,
which means set x=1, so the answer is (1+a)(1+b)(1+c)(1+d)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Mar 28, 2015 at 2:58 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Speaking as a mathematician: the empty product (which is 1 by convention)
> must
> always be included.
>
> (Otherwise the numbers will be ugly)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Sat, Mar 28, 2015 at 2:38 PM, Bob Selcoe <rselcoe at entouchonline.net>
> wrote:
>
>> Hi Seqfans,
>>
>> I was wondering if OEIS-style notation exists for this concept: the sum Z
>> of the products of all combinations of numbers in set S.  Alternatively
>> stated, the sum Z of all nonempty non-proper subset products in set S.
>>
>> For example, S = {3,4,5};  Z = 3 + 4 + 5 + 3*4 + 3*5 + 4*5 + 3*4*5 = 119.
>>
>> I would like to include this concept in some entries as formulas rather
>> than as comments, so notation would be helpful.
>>
>> Thanks in advance,
>> Bob Selcoe
>>
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>
>