generate a specific combinatorial sum symbolically

Luc Meekes wrote: Jean, To (partly) satisfy your curiosity: the expression is part of the denominator of an expression that describes outputs of a specfic n-channel amplifier. In there each Ai is a more complicated expression by itself. Mathcad (11) is capable of solving my entire n-channel amplifier symbolically, sometimes up to n=4, after which I can evaluate solutions numerically, for n=4 and higher (haven't tried to find the limit yet). I want to describe the (full) solution in a way that enables to understand it's structure. So I need a compact description of that specific sum of n summations. That requires I need to "simplify" and you know how good CAS systems are at simplifying.... although I learned a few new tricks in Mathcad along the way. Thanks, Luc

Thanks Luc, for the explanation.

Though I don't understand the logic in such complicated construct, but applied it quick. That would represent a coding of some sort [just a comment to maintain my brain in gear]. Your last part is the permutation, that works symbolically but can't be extracted . We need a brain storm from collabs in there ! Another way to get the permutations is the lexico construct or from tables [Neil Sloane]. But you have to make sure that all the components are really as they reveal up until your expression [4]. If all those components are true, what's left is the symbolic construct of the permutations, for instance the 6 permutations of [a,b,c] = [a,b,c], [a,c,b], [c,a,b], [c,b,a],[b,a,c], [b,c,a] ... most gorgeous would be an "n permute". The rot(v,n) does it but can't be extraced symbolically for a literal module to apply. I'm sure any reader will be interested as already tuned to the challenge. BTW, the centroid member works for any length but it sems you ignore the last term.

Cheers Luc, Jean

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The spell check does not in there , Why ? Don't know.