How Do Stirling Numbers of the First Kind Relate to Combinatorial Formulas?

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Say we have sterling numbers of the first kind where we're given s(n, n-2) = 2(nC3) + 3(nC4)
for n greater than or equal to 4.

I know the left hand side we have n people, and we wish to seat them at n-2 circular tables, but I need help with the right hand side! I would greatly appreciate any help at ALL!
 
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