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

[Bob Selcoe]

Thanks, Neil!  This means what I intended to post was much more convoluted 
and trivial than I realized;  I've offered a (hopefully) appropriate, 
straightforward formula and comment to A139172 which covers everything I 
might have contributed to other related sequences.

Cheers,
Bob

--------------------------------------------------
From: "Neil Sloane" <njasloane at gmail.com>
Sent: Saturday, March 28, 2015 2:01 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Need help with notation: sums of subset products

> 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
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>
>>
>
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