Algebra: Binomial Coefficient
Pascal's triangle
Complete Pascal's triangle \[ \begin{array}{ccc}
n = 0: & & \phantom{0}1 \\
n = 1: & & \phantom{0}1 \quad \phantom{0}1 \\
n = 2: & & \phantom{0}1 \quad \phantom{0}2 \quad \phantom{0}1 \\
n = 3: & & \phantom{0}1 \quad \phantom{0}3 \quad \phantom{0}3 \quad \phantom{0}1 \\
n = 4: & & \phantom{0}1 \quad \phantom{0}4 \quad \phantom{0}6 \quad \phantom{0}4\quad \phantom{0}1 \\
n = 5: & & \phantom{0}1 \quad \phantom{0}5 \quad 10 \quad 10 \quad \phantom{0}5 \quad \phantom{0}1 \\
n = 6: & & \phantom{0}1 \quad \phantom{0}6 \quad 15 \quad 20 \quad 15 \quad \phantom{0}6 \quad \phantom{0}1 \\
\cdots & & \cdots
\end {array}\] with the row for \(n=7\).
Write the answer as a list of length #8#, that is, eight numbers separated by a comma and enclosed by square brackets. An example of this notation is #\rv{1,2,3,4,5,4,3,2}#.
n = 0: & & \phantom{0}1 \\
n = 1: & & \phantom{0}1 \quad \phantom{0}1 \\
n = 2: & & \phantom{0}1 \quad \phantom{0}2 \quad \phantom{0}1 \\
n = 3: & & \phantom{0}1 \quad \phantom{0}3 \quad \phantom{0}3 \quad \phantom{0}1 \\
n = 4: & & \phantom{0}1 \quad \phantom{0}4 \quad \phantom{0}6 \quad \phantom{0}4\quad \phantom{0}1 \\
n = 5: & & \phantom{0}1 \quad \phantom{0}5 \quad 10 \quad 10 \quad \phantom{0}5 \quad \phantom{0}1 \\
n = 6: & & \phantom{0}1 \quad \phantom{0}6 \quad 15 \quad 20 \quad 15 \quad \phantom{0}6 \quad \phantom{0}1 \\
\cdots & & \cdots
\end {array}\] with the row for \(n=7\).
Write the answer as a list of length #8#, that is, eight numbers separated by a comma and enclosed by square brackets. An example of this notation is #\rv{1,2,3,4,5,4,3,2}#.
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