Find the next term in the following sequence. $2, 3, 11, 38, 102, ?$

The pattern is (term number factorial) plus (term number minus one). The first term is $1! + 0 = 2$, the second is $2! + 1 = 3$, the third is $3! + 2 = 8$... Wait, that doesn't match 11. Let's use differences: 3 - 2 = 1, 11 - 3 = 8, 38 - 11 = 27, 102 - 38 = 64. The differences are cubes of 1, 2, 3, and 4, so the next difference is $5^3 = 125$. Adding 125 to 102 gives 227. The result is 227.

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