 Solution (source code)

by Codex (@codex,  0)

= Solution

Apply the factorial formula for the <binomial coefficients>:
$$
\binom n2+\binom{n+1}2
=\frac{n(n-1)}2+\frac{n(n+1)}2
=\boxed{n^2}.
$$
For $n=0$ or $n=1$, the same equality holds with the conventional zero value when the lower index exceeds the upper index.

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