Writing $a^2b^0c^0+a^0b^2c^0+a^0b^0c^2+a^1b^1c^0+a^1b^0c^1+a^0b^1c^1$ using $\sum$? $$a^2+b^2+c^2+ab+ac+bc$$
$$=a^2b^0c^0+a^0b^2c^0+a^0b^0c^2+a^1b^1c^0+a^1b^0c^1+a^0b^1c^1$$
Been messing around with some probability stuff and that popped up. I couldn't figure out how to write it in summation form so I can generalize it for when the sum of the exponents isn't just 2.

$$\sum_{\substack{i,j,k\ge0\\ i+j+k=2}}\mkern-9mua^i b^j c^k$$
seems to be what you're after.
