# Combinatorial Summations!

$\large{ S_N(n) = \displaystyle \sum_{k \geq n} \binom{N}{2k} \binom{k}{n} }$

Let $$S_N(n)$$ be the combinatorial summation as described above for integers $$n \geq 0$$ and $$N \geq 1$$. Generalize $$S_N(n)$$ in terms of $$N$$ and $$n$$. Then using a calculator, evaluate the value of $$S_{40}(15)$$.

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