Challenge to find a identity for the product abc, wherein each term contains a triangular variable as a factor and a, b, c are each separately used as the sole variable of the argument in at least one of the variable triangular numbers.(adsbygoogle = window.adsbygoogle || []).push({});

My solution is

[Tex]abc = T_{(c+ab)} - aT_{b} - T_{c} - b^{2}T_{(a-1)} [/Tex]

Can anyone do better?

Anyone want to try one for the product "abcd"?

FYI T_(x) = x(x+1)/2;

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# Product Identity

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