In a given sequence $\{S_1,S_2,...,S_k\}$, for terms $n\ge3$, the relationship is defined as:
$$ S_n=\sum_{i=1}^{n-1} i\cdot S_{n-i}. $$
For example, if the first two elements are 2 and 3, respectively, the third entry would be $1\cdot3+2\cdot2=7$, and the fourth would be $1\cdot7+2\cdot3+3\cdot2=19$, and so on.

Given that a sequence of integers having this form starts with 2, and the 7th element is 68, what is the second element?

Let's think step by step and output the final answer within \boxed{}.
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