Rows and their sums in code

Build rows of Pascal's triangle in two different ways, and use them to check the sums of the coefficients.

The idea. Each coefficient is the one before it times $\dfrac{n - r + 1}{r}$. The next row comes from adding neighbours. The odd-placed and the even-placed terms of row $n$ each add up to $2^{n - 1}$.

Your tasks.

1. In row, return the coefficients of row n, built place by place with the ratio rule.
2. In next_row, return the row below a given row, using Pascal's rule.
3. In even_odd, return the pair (sum of the odd-placed terms, sum of the even-placed terms) of row n.