Mad factorials!

\[\large \left( \sum_{n=1}^{2017!+1}(n^{2017}!!)\right)^{2017!!} \]

Find the sum of last two digits of the expression above .

Notation :

  • \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

  • \(!!\) denotes the double factorial notation :

    For an even number & \(n>0\), \(n!!=n\times (n-2)\times \cdots\times 4\times 2.\)

    For an odd number & \(n>0\), \(n!!=n\times (n-2)\times \cdots\times 3\times 1.\)

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