Find the missing term in the given sequence. $4, 9, 29, ?, 599, 3599$

The pattern multiplies the previous term by an integer and then subtracts a sequentially increasing number. Multiplying 4 by 3 and subtracting 3 gives 9; multiplying 9 by 4 and subtracting 7 gives 29. Multiplying 29 by 5 and subtracting 11 gives 134. Multiplying 134 by 6 and subtracting 15 gives 789, which does not equal 599. Let's test option A: multiplying 29 by 3 and adding 30 gives 117. Multiplying 117 by 5 and adding 10 gives 595, which does not equal 599. The actual sequence is $1! + 3$, $2! + 7$, $3! + 23$, $4! + 95$, $5! + 479$. The missing term is not listed in the options. The result is None of these.

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