Binomial Sum

Algebra Level pending

\[3^2 \binom{20}{3}+6^2 \binom{20}{6}+9^2 \binom{20}{9}+ \cdots +18^2 \binom{20}{18}=k(2^{18}-1)\]

Here, \(k\) is a positive integer. Find \(k\).

Note : Please refrain from using Wolfram Alpha or similar software to solve this problem.

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