Expansion?

Find the coefficient of \(t^{24}\) in the expansion of \((1+t^{2})^{12}(1+t^{12})(1+t^{24})\).

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Notation: \( \dbinom MN \) denotes the binomial coefficient, \( \dbinom MN = \dfrac{M!}{N!(M-N)!} \).

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