APL (Dyalog Unicode), 16 12 bytes^SBCS

Anonymous tacit prefix function. Assumes ⎕IO (Index Origin) to be 0, which is default on many systems. 1-indexed.

+/⊢↑∘∊¯1,¨⍨⍳ 

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+/ the sum of

⊢↑ the first n elements

∘∊ of the ϵnlisted (flattened)

¯1,¨⍨ negative-one-appended-to-each

⍳ first n ɩndices (0 through n–1