Forest Math Gate

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Answer the question exactly to open the path.

Very hard math question

How many onto functions f: {1, 2, …, 15} → {1, 2, …, 6} exist? Enter the exact integer value.

Need a hint?

The count of onto functions (surjections) from an n-element set to a k-element set is S(n,k)·k! = ∑(i=0..k) (-1)^i · C(k,i) · (k - i)^n.