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Default changing rows *and* columns in automatic formulae

Suppose I have an nxn square table; and I want to create a list that will tell me, for the jth row, the sum of the first j columns.

With what I know at the moment (pretty limited) I could enter a formula, and drag to get either a row or a column of data; but since I'm actually changing row-dependent and column-dependent info for each thing, either way I'm going to have to go through manually and either extend the range of the sum (if I'm dragging down to get a column) or change the row being summed (if I'm dragging across to get a row).

Is there any way to enter the formula so that, say, when I drag down to create a column of values, I don't have to go through and manually edit each one?

Thanks for any help - hope my explanation of the problem isn't too muddled!
 
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