How to write two for loops in math notation?

I have a vector of numbers that looks like this:

[1, 2, 3, 4, 5]

For every number the vector, I would like to multiply each number by every other number and find the sum:

1*1 + 1*2 + 1*3 + 1*4 + 1*5 + 2*1 + 2*2 + 2*3 + 2*4 + 2*5 + ... + 5*5

How can I write this in math notation?

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