jmc

The row 1, 1 has 2 numbers. The row 1, 2, 1 has 3 numbers. The row 1, 3, 3, 1 has 4 numbers. Each time we go down one row, we have one more number in the list. So, the row that starts 1, $k$ has $k+1$ numbers (namely, the numbers $\left(\genfrac{}{}{0ex}{}{k}{0}\right),\left(\genfrac{}{}{0ex}{}{k}{1}\right),\left(\genfrac{}{}{0ex}{}{k}{2}\right),\dots ,\left(\genfrac{}{}{0ex}{}{k}{k}\right)$.) So the row with 43 numbers starts 1, $\boxed{42}$.