Write a function `multiplication_table_row(n)` that takes a positive integer `n` and returns a list of integers representing the row `n` of a standard multiplication table (where rows and columns start at 1). The row should contain `n` elements: `[1*n, 2*n, 3*n, ..., n*n]`.
For example, if `n = 3`, the row is `[3, 6, 9]`.
Your function should handle any positive integer `n` (1 ≤ n ≤ 1000).